• Oct 13, 2019

10 Steps to Problem Solving for Engineers

Updated: Dec 6, 2020

With the official launch of the engineering book 10+1 Steps to Problem Solving: An Engineer's Guide it may be interesting to know that formalization of the concept began in episode 2 of the Engineering IRL Podcast back in July 2018.

As noted in the book remnants of the steps had existed throughout my career and in this episode I actually recorded the episode off the top of my head.

My goal was to help engineers build a practical approach to problem solving.

Have a listen.

Who can advise on the best approach to problem solving other than the professional problem solvers - Yes. I'm talking about being an Engineer.

There are 2 main trains of thought with Engineering work for non-engineers and that's trying to change the world with leading edge tech and innovations, or plain old boring math nerd type things.

Whilst, somewhat the case what this means is most content I read around Tech and Engineering are either super technical and (excruciatingly) detailed. OR really riff raff at the high level reveling at the possibilities of changing the world as we know it. And so what we end up with is a base (engineer only details) and the topping (media innovation coverage) but what about the meat? The contents?

There's a lot of beauty and interesting things there too. And what's the centrepiece? The common ground between all engineers? Problem solving.

The number one thing an Engineer does is problem solving. Now you may say, "hey, that's the same as my profession" - well this would be true for virtually every single profession on earth. This is not saying there isn't problem solving required in other professions. Some problems require very basic problem solving techniques such is used in every day life, but sometimes problems get more complicated, maybe they involve other parties, maybe its a specific quirk of the system in a specific scenario. One thing you learn in engineering is that not all problems are equal. These are

 The stages of problem solving like a pro:

Is the problem identified (no, really, are you actually asking the right question?)

Have you applied related troubleshooting step to above problem?

Have you applied basic troubleshooting steps (i.e. check if its plugged in, turned it on and off again, checked your basics)

Tried step 2 again? (Desperation seeps in, but check your bases)

Asked a colleague or someone else that may have dealt with your problem? (50/50 at this point)

Asked DR. Google (This is still ok)

Deployed RTFM protocol (Read the F***ing Manual - Engineers are notorious for not doing this)

Repeated tests, changing slight things, checking relation to time, or number of people, or location or environment (we are getting DEEP now)

Go to the bottom level, in networking this is packet sniffers to inspect packets, in systems this is taking systems apart and testing in isolation, in software this is checking if 1 equals 1, you are trying to prove basic human facts that everyone knows. If 1 is not equal to 1, you're in deep trouble.At this point you are at rebuild from scratch, re install, start again as your answer (extremely expensive, very rare)

And there you have it! Those are your levels of problem solving. As you go through each step, the more expensive the problem is. -- BUT WAIT. I picked something up along the way and this is where I typically thrive. Somewhere between problem solving step 8 and 10. 

how to solve an engineering problem

The secret step

My recommendation at this point is to try tests that are seemingly unrelated to anything to do with the problem at all.Pull a random cable, test with a random system off/on, try it at a specific time of the day, try it specifically after restarting or replugging something in. Now, not completely random but within some sort of scope. These test are the ones that when someone is having a problem when you suggest they say "that shouldn't fix the problem, that shouldn't be related" and they are absolutely correct.But here's the thing -- at this stage they have already tried everything that SHOULD fix the problem. Now it's time for the hail mary's, the long shots, the clutching at straws. This method works wonders for many reasons. 1. You really are trying to try "anything" at this point.

2. Most of the time we may think we have problem solving step number 1 covered, but we really don't.

3. Triggering correlations.

This is important.

Triggering correlations

In a later post I will cover correlation vs causation, but for now understand that sometimes all you want to do is throw in new inputs to the system or problem you are solving in order to get clues or re identify problems or give new ways to approach earlier problem solving steps. There you have it. Problem solve like a ninja. Approach that extremely experienced and smart person what their problem and as they describe all the things they've tried, throw in a random thing they haven't tried. And when they say, well that shouldn't fix it, you ask them, well if you've exhausted everything that should  have worked, this is the time to try things that shouldn't. Either they will think of more tests they haven't considered so as to avoid doing your preposterous idea OR they try it and get a new clue to their problem. Heck, at worst they confirm that they do know SOMETHING about the system.

Go out and problem solve ! As always, thanks for reading and good luck with all of your side hustles.

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  • TeachEngineering
  • Problem Solving

Lesson Problem Solving

Grade Level: 8 (6-8)

(two 40-minute class periods)

Lesson Dependency: The Energy Problem

Subject Areas: Physical Science, Science and Technology

Partial design

  • Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

  • Energy Forms and States Demonstrations
  • Energy Conversions
  • Watt Meters to Measure Energy Consumption
  • Household Energy Audit
  • Light vs. Heat Bulbs
  • Efficiency of an Electromechanical System
  • Efficiency of a Water Heating System
  • Solving Energy Problems
  • Energy Projects

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Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, introduction/motivation, associated activities, user comments & tips.

Engineering… designed to work wonders

Scientists, engineers and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

  • Students demonstrate an understanding of the Technological Method of Problem Solving.
  • Students are able to apply the Technological Method of Problem Solving to a real-life problem.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science.

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International Technology and Engineering Educators Association - Technology

State standards, national science education standards - science.

Scientists, engineers, and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

In this unit, we use what is called "The Technological Method of Problem Solving." This is a seven-step procedure that is highly iterative—you may go back and forth among the listed steps, and may not always follow them in order. Remember that in most engineering projects, more than one good answer exists. The goal is to get to the best solution for a given problem. Following the lesson conduct the associated activities Egg Drop and Solving Energy Problems for students to employ problem solving methods and techniques. 

Lesson Background and Concepts for Teachers

The overall concept that is important in this lesson is: Using a standard method or procedure to solve problems makes the process easier and more effective.

1) Describe the problem, 2) describe the results you want, 3) gather information, 4) think of solutions, 5) choose the best solution, 6) implement the solution, 7) evaluate results and make necessary changes. Reenter the design spiral at any step to revise as necessary.

The specific process of problem solving used in this unit was adapted from an eighth-grade technology textbook written for New York State standard technology curriculum. The process is shown in Figure 1, with details included below. The spiral shape shows that this is an iterative, not linear, process. The process can skip ahead (for example, build a model early in the process to test a proof of concept) and go backwards (learn more about the problem or potential solutions if early ideas do not work well).

This process provides a reference that can be reiterated throughout the unit as students learn new material or ideas that are relevant to the completion of their unit projects.

Brainstorming about what we know about a problem or project and what we need to find out to move forward in a project is often a good starting point when faced with a new problem. This type of questioning provides a basis and relevance that is useful in other energy science and technology units. In this unit, the general problem that is addressed is the fact that Americans use a lot of energy, with the consequences that we have a dwindling supply of fossil fuels, and we are emitting a lot of carbon dioxide and other air pollutants. The specific project that students are assigned to address is an aspect of this problem that requires them to identify an action they can take in their own live to reduce their overall energy (or fossil fuel) consumption.

The Seven Steps of Problem Solving

1.  Identify the problem

Clearly state the problem. (Short, sweet and to the point. This is the "big picture" problem, not the specific project you have been assigned.)

2.  Establish what you want to achieve

  • Completion of a specific project that will help to solve the overall problem.
  • In one sentence answer the following question: How will I know I've completed this project?
  • List criteria and constraints: Criteria are things you want the solution to have. Constraints are limitations, sometimes called specifications, or restrictions that should be part of the solution. They could be the type of materials, the size or weight the solution must meet, the specific tools or machines you have available, time you have to complete the task and cost of construction or materials.

3.  Gather information and research

  • Research is sometimes needed both to better understand the problem itself as well as possible solutions.
  • Don't reinvent the wheel – looking at other solutions can lead to better solutions.
  • Use past experiences.

4.  Brainstorm possible solutions

List and/or sketch (as appropriate) as many solutions as you can think of.

5.  Choose the best solution

Evaluate solution by: 1) Comparing possible solution against constraints and criteria 2) Making trade-offs to identify "best."

6.  Implement the solution

  • Develop plans that include (as required): drawings with measurements, details of construction, construction procedure.
  • Define tasks and resources necessary for implementation.
  • Implement actual plan as appropriate for your particular project.

7.  Test and evaluate the solution

  • Compare the solution against the criteria and constraints.
  • Define how you might modify the solution for different or better results.
  • Egg Drop - Use this demonstration or activity to introduce and use the problem solving method. Encourages creative design.
  • Solving Energy Problems - Unit project is assigned and students begin with problem solving techniques to begin to address project. Mostly they learn that they do not know enough yet to solve the problem.
  • Energy Projects - Students use what they learned about energy systems to create a project related to identifying and carrying out a personal change to reduce energy consumption.

The results of the problem solving activity provide a basis for the entire semester project. Collect and review the worksheets to make sure that students are started on the right track.

how to solve an engineering problem

Learn the basics of the analysis of forces engineers perform at the truss joints to calculate the strength of a truss bridge known as the “method of joints.” Find the tensions and compressions to solve systems of linear equations where the size depends on the number of elements and nodes in the trus...

preview of 'Doing the Math: Analysis of Forces in a Truss Bridge' Lesson

Through role playing and problem solving, this lesson sets the stage for a friendly competition between groups to design and build a shielding device to protect humans traveling in space. The instructor asks students—how might we design radiation shielding for space travel?

preview of 'Shielding from Cosmic Radiation: Space Agency Scenario' Lesson

A process for technical problem solving is introduced and applied to a fun demonstration. Given the success with the demo, the iterative nature of the process can be illustrated.

preview of 'Egg Drop' Activity

The culminating energy project is introduced and the technical problem solving process is applied to get students started on the project. By the end of the class, students should have a good perspective on what they have already learned and what they still need to learn to complete the project.

preview of 'Solving Energy Problems' Activity

Hacker, M, Barden B., Living with Technology , 2nd edition. Albany NY: Delmar Publishers, 1993.

Other Related Information

This lesson was originally published by the Clarkson University K-12 Project Based Learning Partnership Program and may be accessed at http://internal.clarkson.edu/highschool/k12/project/energysystems.html.


Supporting program, acknowledgements.

This lesson was developed under National Science Foundation grants no. DUE 0428127 and DGE 0338216. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

Last modified: August 16, 2023

Engineering Passion

Tips for Solving Engineering Problems Effectively

how to solve an engineering problem

Problem solving is the process of determining the best feasible action to take in a given situation. Problem solving is an essential skill for engineers to have. Engineers are problem solvers, as the popular quote says:

“Engineers like to solve problems. If there are no problems handily available, they will create their own problems.” – Scott Adams

Engineers are faced with a range of problems in their everyday life. The nature of problems that engineers must solve differs between and among the various disciplines of engineering. Because of the diversity of problems there is no universal list of procedures that will fit every engineering problem. Engineers use various approaches while solving problems.

Engineering problems must be approached systematically, applying an algorithm, or step-by-step practice by which one arrives at a feasible solution. In this post, we’ve prepared a list of tips for solving engineering problems effectively.

#1 Identify the Problem

Identify the Problem

Evaluating the needs or identifying the problem is a key step in finding a solution for engineering problems. Recognize and describe the problem accurately by exploring it thoroughly. Define what question is to be answered and what outputs or results are to be produced. Also determine the available data and information about the problem in hand.

An improper definition of the problem will cause the engineer to waste time, lengthen the problem solving process and finally arrive at an incorrect solution. It is essential that the stated needs be real needs.

As an engineer, you should also be careful not to make the problem pointlessly bound. Placing too many limitations on the problem may make the solution extremely complex and tough or impossible to solve. To put it simply, eliminate the unnecessary details and only keep relevant details and the root problem.

#2 Collect Relevant Information and Data

Collect Relevant Information and Data

After defining the problem, an engineer begins to collect all the relevant information and data needed to solve the problem. The collected data could be physical measurements, maps, outcomes of laboratory experiments, patents, results of conducted surveys, or any number of other types of information. Verify the accuracy of the collected data and information.

As an engineer, you should always try to build on what has already been done before. Don’t reinvent the wheel. Information on related problems that have been solved or unsolved earlier, may help engineers find the optimal solution for a given problem.

#3 Search for Creative Solutions

Search for Creative Solutions

There are a number of methods to help a group or individual to produce original creative ideas. The development of these new ideas may come from creativity, a subconscious effort, or innovation, a conscious effort.

You can try to visualize the problem or make a conceptual model for the given problem. So think of visualizing the given problem and see if that can help you gain more knowledge about the problem.

#4 Develop a Mathematical Model

Develop a Mathematical Model

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application.

To develop a mathematical model for the problem, determine what basic principles are applicable and then draw sketches or block diagrams to better understand the problem. Then define and introduce the necessary variables so that the problem is stated purely in mathematical terms.

Afterwards, simplify the problem so that you can obtain the required result. Also identify the and justify the assumptions and constraints in the mathematical model.

#5 Use Computational Method

Use Computational Method

You can use a computational method based on the mathematical method you’ve developed for the problem. Derive a set of equations that enable the calculation of the desired parameters and variables as described in your mathematical model. You can also develop an algorithm, or step-by-step procedure of evaluating the equations involved in the solution.

To do so, describe the algorithm in mathematical terms and then execute it as a computer program.

#6 Repeat the Problem Solving Process

Repeat the Problem Solving Process

Not every problem solving is immediately successful. Problems aren’t always solved appropriately the first time. You’ve to rethink and repeat the problem solving process or choose an alternative solution or approach to solving the problem.


Engineers often use the reverse-engineering method to solve problems. For example, by taking things apart to identify a problem, finding a solution and then putting the object back together again. Engineers are creative , they know how things work, and so they constantly analyze things and discover how they work.

Problem-solving skills help you to resolve obstacles in a situation. As stated earlier, problem solving is a skill that an engineer must have and fortunately it’s a skill that can be learned. This skill gives engineers a mechanism for identifying things, figuring out why they are broken and determining a course of action to fix them.

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How to Solve Engineering Problems


Introduction: How to Solve Engineering Problems

How to Solve Engineering Problems

These Instructables have been created in order to help young, aspiring engineers develop a critical skill set that will help them through their schooling and throughout their careers.  This skill set will become a repetitive process that can be applied over and over again to any problem that they may encounter at any time.  These instructions are not limited to only engineers however, as many professionals or other students can find these useful for solving problems in their respective fields.  For the purpose of this Instructable, I will walk you through the generic steps that should be taken in this process and then I will solve an engineering related problem using these steps. The picture below shows how complex a design can be, but using the following method can take something this complex and break it into simpler parts while keeping it a beautiful design.  Thanks to http://farm3.static.flickr.com/2383/2518751632_53119dfd58.jpg for providing the picture!

Step 1: Materials Needed

Materials Needed

For a majority of these problems, only a few things are needed to help you solve them.  They are a calculator, scale, paper, and pencil.  This may sound like very little supplies but it really is all that one needs.  I would recommend a scientific calculator for these problems since they will most likely contain equations that are too difficult to be handled by a simple calculator.  Any kind of paper will work but grid paper is generally the most useful so you can keep things organized vertically and horizontally.  If you do not have a scale, a plain ruler will suffice.  The scale/ruler will help you keep your schematic drawings neat and easy for both you and your professor/boss to follow.

Step 2: Problem Statement

Problem Statement

Once you have collected everything that you need to solve the problem, you need to read through it.  This is a vital step in the overall process.  Numerous young engineers have a tendency to simply scan the problem, but this poses a problem since they end up missing information that would likely make the problem simpler.  The best thing to do for this step is read the problem thoroughly and to read it twice, making sure that you have gathered all the information.

Step 3: Given/Find


After reading through the problem two or three times, it is important for you to extract all the necessary information.  List out what you have or what is given to you.  This can be constraints, variables, values, or even equations that link some of the variables together.  It is important for you to list all these things so that you will not have to continuously scan the problem over and over looking for certain values. After you list your given information, make sure you understand what is being asked.  For most problems (like the one I am working through), it is directly asked to you to find something.  Make sure you write this down as you are working to ensure you do not solve something you do not need.

Step 4: Assumptions


Once you have completed the previous steps, you need to make a list of acceptable assumptions for your problem.  It is important to remember to work easier not harder!  Assumptions allow you to make your complex problem a simpler model which will give results that are just as valid.  However, it is also important that you do not make assumptions that will make your results unacceptable.  This is the most difficult step of the skill set to grow accustomed to.  It takes time, practice, and patience to understand what assumptions become acceptable and what ones do not!

Step 5: Schematic Drawings

Schematic Drawings

Once you have read through the problem, defined what was given and what needs to be found, and listed your assumptions, you need to create a schematic.  The schematic drawing or drawings allow you to physically see what is happening in the problem.  This can help you as you begin to go through your equations and analysis, as well as helping you verify your answers once you get them.  You will be able to go back and check your values to ensure that everything.

Step 6: Equations/Analysis


This step is the one that most young engineers immediately jump into when trying to solve problems.  However, as you have seen, this should be one of the last steps that are taken.  For this step, first write out the equations that you will be using.  There is no need to solve them just yet, write out the equations in their variable form.  This will allow you to make sure you have all the information you need to solve that equation.  If you do not, you will need to find another equation or equations that solve for the unknown variable/variables. The second part of this step is to actually solve your equations, whether it is one equation or five equations simultaneously.  In some instances, your question may ask for multiple variables or it may just ask for one variable.  This is where all of your work finally begins to make sense and you can see how your problem is finishing up.  Solving should be one of the easier steps, all you should have to do is plug the values into your calculator and get the results.

Step 7: Results


Here is the step that everyone just wants to get to!  You finally get to see your results for all of the work that you have put in.  It is important to make sure that your results are easy to see, so a lot of people prefer either a double underline under the result or a box around it.  This makes it easy to find and leaves no question as to what your answer might or might not be.

Step 8: Verification

After you have completed all steps up to this point, you only have one left!  Verifying your answer is a big step for a couple of different reasons.  One reason that it is so important to verify your results is to make sure that your answer makes sense.  For example, if a flow should be in the positive x-direction, a negative answer would imply that the flow is going opposite of what it should.  It is also important to verify your results to make sure that your answer has proper units.  It would not be a legitimate answer if you had units for velocity (m/s) for a problem where you were trying to solve for a force (N).  The last reason it is important to verify your results is that it is a good habit to get into before you enter the workplace.  Here, you will need to make sure your answers are right and that they make sense since you can be held accountable for your work.

how to solve an engineering problem

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3 years ago

Very good approach in solving engineering design problem. I really like it. I have a problem that I have been trying to solve, can I get help?


Question 3 years ago on Step 2

Please I need guide to solving this problem


12 years ago on Introduction

Once I believed I wanted to be an electrical engineer, but decided against it in favor of becoming a pastor. Thank you for a glimpse of what is involved in solving engineering problems, although this is not from anything electrical. I was especially interested in the latter parts dealing with verifying the solution. In many situations I am distressed at myself for doing something too quickly and arriving at an erroneous solution to a problem.


12 years ago on Step 8

Wow! Amilte, This is one of the problems I solved on my Heat and Mass transfer course at the technikon. Thanks, I do my continous practice almost everyday where I select at least 3 problems per day. Thanks once again

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  • Steps in solving well-defined engineering process problems, including textbook problems
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Engineering Problem Solving ¶

Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them. —Laurence J. Peter

Steps in solving ‘real world’ engineering problems ¶

The following are the steps as enumerated in your textbook:

Collaboratively define the problem

List possible solutions

Evaluate and rank the possible solutions

Develop a detailed plan for the most attractive solution(s)

Re-evaluate the plan to check desirability

Implement the plan

Check the results

A critical part of the analysis process is the ‘last’ step: checking and verifying the results.

Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).

In a practical sense, these checks must be part of a comprehensive risk management strategy.

My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).

In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …

Exercise: Problem solving

Step 3 above refers to ranking of alternatives.

Think of an existing product of interest.

What do you think was ranked highest when the product was developed?

Consider what would have happened if a different ranking was used. What would have changed about the product?

Brainstorm ideas with the students around you.

Defining problems collaboratively ¶

Especially in light of global engineering , we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:

Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”

Location : Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?

Knowledge : What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?

Desire : What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?

As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.

Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.

To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?

How ‘good’ a solution do you need ¶

There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.

This is difficult to assess without some experience in the particular environment.

How ‘Good’ a Solution Do You Need?

Some rough examples:

10 second answer (answering a question at a meeting in front of your manager or vice president)

10 minute answer (answering a quick question from a colleague)

10 hour answer (answering a request from an important customer)

10 day answer (assembling information as part of a trouble-shooting team)

10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)

Steps in solving well-defined engineering process problems, including textbook problems ¶

Essential steps:

Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.

Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.

Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.

Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.

Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.

Write down all equations in their general forms. Don’t simplify anything yet.

Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.

Replace remaining terms with more convenient forms (because of the given information or selected symbols).

Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.

Whenever possible, solve the equations for the unknown(s) algebraically .

Convert the units of your variables as needed to have a consistent set across your equations.

Substitute these values into the equation(s) from step 7 to get numerical results.

Check your answer.

Does it make sense?

Are the units of the answer correct?

Is the answer consistent with other information you have?

Exercise: Checking results

How do you know your answer is right and that your analysis is correct?

This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?

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An Inquiry-Based Introduction to Engineering pp 71–78 Cite as

Engineering Problem-Solving

  • Michelle Blum 2  
  • First Online: 21 September 2022

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You are becoming an engineer to become a problem solver. That is why employers will hire you. Since problem-solving is an essential portion of the engineering profession, it is necessary to learn approaches that will lead to an acceptable resolution. In real-life, the problems engineers solve can vary from simple single solution problems to complex opened ended ones. Whether simple or complex, problem-solving involves knowledge, experience, and creativity. In college, you will learn prescribed processes you can follow to improve your problem-solving abilities. Also, you will be required to solve an immense amount of practice and homework problems to give you experience in problem-solving. This chapter introduces problem analysis, organization, and presentation in the context of the problems you will solve throughout your undergraduate education.

  • Research Problem
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  • Troubleshooting Problem
  • Mathematics Problem
  • Resource Problem
  • Societal Problem
  • Personal Problem
  • Design Problems
  • Problem-Solving Technique
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https://www.merriam-webster.com/dictionary , viewed June 3, 2021.

Mark Thomas Holtzapple, W. Dan Reece (2000), Foundations of Engineering, McGraw-Hill, New York, New York, ISBN:978-0-07-029706-7.

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End of Chapter Problems

1.1 ibl questions.

IBL1: Using standard problem-solving technique, answer the following questions

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, draw the vector representation of your path (hint: use a compass legend to help create your coordinate system)

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, explain how to calculate the velocity you ran in the north direction.

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, explain how to calculate the velocity you ran in the east direction.

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, explain how to calculate how far you ran in the north direction.

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, explain how to calculate how far you ran in the east direction.

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, how far north have you traveled in 5 min?

If you run in a straight line at a velocity of 10 mph in a direction of 35 degree North of East, how far east have you traveled in 5 min?

What type of problem did you solve?

IBL2: For the following scenarios, explain what type of problem it is that needs to be solved.

Scientists hypothesize that PFAS chemicals in lawn care products are leading to an increase in toxic algae blooms in lakes during summer weather.

An engineer notices that a manufacturing machine motor hums every time the fluorescent floor lights are turned on.

The U.N. warns that food production must be increased by 60% by 2050 to keep up with population growth demand.

Engineers are working to identify and create viable alternative energy sources to combat climate change.

1.2 Practice Problems

Make sure all problems are written up using appropriate problem-solving technique and presentation.

The principle of conservation of energy states that the sum of the kinetic energy and potential energy of the initial and final states of an object is the same. If an engineering student was riding in a 200 kg roller coaster car that started from rest at 10 m above the ground, what is the velocity of the car when it drops to 2.5 m above the ground?

Archimedes’ principle states that the total mass of a floating object equals the mass of the fluid displaced by the object. A 45 cm cylindrical buoy is floating vertically in the water. If the water density is 1.00 g/cm 3 and the buoy plastic has a density of 0.92 g/cm 3 determine the length of the buoy that is not submerged underwater.

A student throws their textbook off a bridge that is 30 ft high. How long would it take before the book hits the ground?

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7 Surprising Ways Engineering Has Solved Everyday Problems

Engineer with lots of tools taking notes

We live in a hacking culture where we break down and repurpose everything from IKEA furniture to power tools, redesigning them to fill a need or solve a problem for which they were not originally intended. By applying some of the basic design-cycle steps of Ask, Research, Imagine, Plan, Create, Test and Improve, engineering-minded product designers are turning what might have once been considered science fictional solutions into reality.

By sharpening your engineering skill set , you can put yourself in a unique position to address some pervasive everyday problems. Which would you like to take on? For a little inspiration, take a look at some real-world everyday challenges, big and small, that have been alleviated by some rather innovative engineering solutions.

Squeezing Out the Last Drop of Liquid

We’ve all experienced the frustration of attempting to squeeze the last drop of ketchup or toothpaste from their containers. That could end very soon, all thanks to a unique slippery coating that keeps thick, gooey substances from sticking to solid surfaces.

Called LiquiGlide, this material was initially was created to line oil and gas pipelines to protect against buildup. 1 It worked so well that the team developing this technology at MIT decided to explore other commercial applications for it. They researched and tested different combinations of materials to create new variations of LiquiGlide, including food-grade and medical-grade versions. These can help reduce product waste and enable viscous liquid medications to efficiently empty from tubes to improve proper dosing.

Holding Hot Coffee Without Spilling It

The coffee cup sleeve: With such deceptively simple design and such obvious value, it’s hard to believe it wasn’t invented sooner than it was, back in 1991. The idea was born two years prior, when piping hot coffee in a paper to-go cup burned the hands (and subsequently spilled on the lap) of future Java Jacket founder Jay Sorensen.

Sorensen did considerable research on the potential market demand for such a product, the kinds of materials that could be used to cost-effectively create it and the most successful physical design. He produced and tested several iterations of the sleeve before landing on the prototype that is still used today. 2 Now, the nearly ubiquitous coffee cup sleeves are helping save the fingers (and laps) of countless hot-java-drinking commuters—not to mention engineers.

A Far-Reaching Solve for Getting the Group Shot

By freeing us from having to rely on a willing passerby to take a group photo in front of a tourist attraction or a silhouette shot against a stunning sunset, the selfie stick has certainly made an impact in today’s social-media-savvy world.

Wayne Fromm didn’t invent camera-on-a-stick technology, but in 2005 he did patent a version that could hold almost any camera and, eventually, nearly any smartphone. 3 That’s the version that began to resonate with consumers worldwide.

Since then, the original selfie stick concept has evolved into several iterations by Fromm and other manufacturers to answer the demand for more uses—including ones that extend telescopically at the push of a button so you can fit more people or more background into your shot, that allow you to snap a shot via Bluetooth without needing to set the camera timer, or that take blur-free photographs and video while skydiving or partaking in other action sports.

Walking Your Way to Health at Work

Dr. James Levine, a medical doctor who researches obesity, found that sitting for several hours at a time negatively impacts our health much more than initially thought, even for those who regularly go to the gym. He argued that our increasingly sedentary lifestyle, fueled by demands at work requiring us to be at our desks, has contributed to a culture of people with poor posture, lack of energy, and increased risk of heart disease and diabetes.

Levine came up with a rather unusual solution: He rigged a used treadmill under a raised bedside tray. 4 Perhaps this prototype he created in 1999 wasn’t the most attractive setup, but its goal was clear: to give people a way to be active while working and help reduce sitting-related health risks.

Levine worked with a manufacturer to produce the first official treadmill desk, released in 2007. Today, many companies promoting a healthier workplace offer employees the option to have such a desk instead of a traditional one.

Overcoming Fear of Public Speaking

Sophia Velastegui, an influential engineer in the technology sector, applied several engineering design steps early in her career to conquer a common phobia: speaking in front of a crowd. 5

Velastegui did this by:

  • Identifying specific problems to address: her shyness and fear of public speaking
  • Looking into ways to work on them (such as volunteering to speak at company meetings)
  • Setting up a plan of action to overcome her shyness with strangers: research people to meet at conferences, contact them, choose discussion topics and maintain regular contact
  • Continuing to improve her speaking and networking skills through constant practice

Velastegui’s process improved her public speaking—and her confidence and management skills—so thoroughly that it has been invaluable to her rise through desirable positions at top companies. Not only that, she was named to Business Insider's list of most powerful female engineers in 2017.

Eating With Confidence, Without Spilling

Many of us take the simple act of feeding ourselves for granted. But for anyone with trembling hands, it can be a frustrating struggle to keep food on a fork or spoon long enough to reach their mouth without it winding up on the table or their clothing. Liftware Level™ utensils were created by inventors with loved ones experiencing such limitations.

Liftware uses sensor technology that makes real-time adjustments to accommodate any mild-to-severe shaking and trembling movements. 6 This improves accessibility and independence for those suffering from conditions such as Parkinson’s disease.

Liftware developers are taking their testing to a new level: They created an app that records motion data using an accelerometer sensor found in smartphones. They use this data when creating prototypes for versions of other common products that can be used by people with disabilities.

Diagnosing Deep Gastrointestinal Diseases

In 1981, inspired by a friend experiencing small intestine pain with no apparent source, rocket engineer Gavriel Iddan wondered if there was a way to create a “missile”—complete with a camera—that could be launched into the intestine to snap photographs in order to help physicians make accurate diagnoses.

Applying his knowledge of rocket engineering to a completely unrelated problem led to his invention of the ingestible camera. “PillCam” actually took 17 years to become reality, thanks to Iddan’s diligence and the development of micro cameras, transmitters and LED lights that could fit into a large pill-sized capsule. 7

Now the diagnostic standard, doctors can properly identify conditions that are deep in the digestive tract, areas previously unreachable by other nonsurgical methods.

Put Your Engineering Skills to Use

The world is full of countless challenges waiting for that one solution to be created or tweaked that can make life just a little easier, healthier or better. What problems are you planning on tackling with an engineering approach? What inefficiencies are you improving? And better yet, how many more opportunities might present themselves as you continue to hone your engineering expertise?

Using your engineering knowledge, there’s no limit to what you can do. Explore our online graduate engineering degree programs at Case Western Reserve University to get started improving the world around you today.

  • Retrieved on September 8, 2018, from liquiglide.com/
  • Retrieved on September 8, 2018, from smithsonianmag.com/arts-culture/how-the-coffee-cup-sleeve-was-invented-119479/
  • Retrieved on September 8, 2018, from businessinsider.com/wayne-fromm-is-the-inventor-of-the-modern-selfie-stick-2015-8
  • Retrieved on September 8, 2018, from newyorker.com/magazine/2013/05/20/the-walking-alive
  • Retrieved on September 8, 2018, from businessinsider.com/how-this-engineer-hacked-her-career-and-became-a-gm-at-microsoft-2018-2
  • Retrieved on September 8, 2018, from launchforth.io/blog/post/invention-spotlight-liftware-level/2335/
  • Retrieved on September 8, 2018, from epo.org/learning-events/european-inventor/finalists/2011/iddan/impact.html

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7 Engineering Challenges Design Thinking Can Help Solve

Engineer seated at desk using computer

  • 19 Jan 2023

Several challenges face the engineering industry. Addressing them requires innovative solutions and structured processes, such as design thinking.

If you’re an engineer who wants to develop business skills , here's an overview of design thinking and seven engineering challenges it can help solve.

What Is Design Thinking?

Design thinking is one of the most effective approaches to problem-solving. It’s a solutions-based methodology focused on human-centered design and observing problems with empathy.

In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar structures the process using a four-stage framework. The stages are:

Graphic showing design thinking's four stages: clarify, ideate, develop, and implement

In the clarification stage, you observe a situation or challenge without bias and frame your findings in the form of a problem statement.

“Before you begin to generate innovative solutions for your own design problem, you must always think hard about how you’re going to frame that problem,” Datar says in the course.

Reframing the problem as a question is an excellent way to do this. For example, using "how might we" instead of "the problem is" can encourage empathy in the design process and shift your mindset toward potential solutions.

These questions are particularly important when considering empathetic design. According to the Harvard Business Review , engineers who put themselves in their audience's shoes while designing often develop innovative products . By understanding your audience’s unexpressed needs, you can effectively leverage your technical knowledge to create innovative solutions to previously unknown problems.

Once you've made your observations, you can explore potential solutions. The ideate stage is for divergent thinking—the process of exploring as many ideas as possible. It involves:

  • Finding and categorizing similarities in users' pain points
  • Considering the resources available to you and how you can use them to solve a problem
  • Brainstorming potential solutions

Creativity and an open mind are vital at this stage. As you explore ideas, they can highlight other problems you were unaware of.

The development stage focuses on turning your ideas into workable prototypes. For ideas to be innovative, they must be both new and useful ; many, though creative, aren't feasible.

"As you prototype concepts in phase three, you may discover results that force you to return to phases one and two to reframe your question," Datar says in Design Thinking and Innovation .

This iteration can occur in any of the four stages because each involves a different level of exploration that highlights new problems, questions, or solutions. This isn't cause for discouragement.

"Do not think of this as a setback,” Datar says in the course. “Iterating on solutions is a normal and expected result of design thinking.”

Design thinking’s ultimate objective is finding effective, workable solutions. The implementation phase involves finalizing developments and communicating their value to stakeholders.

This final stage can be challenging for many engineers. Since their work is so technical, it’s sometimes difficult for stakeholders to understand their impact on the organization. As a result, engineers should develop effective communication skills to ensure their ideas are implemented.

The Importance of Design Thinking in Engineering

Design thinking is a valuable skill for engineers to learn for several reasons. For one, engineering positions are among the most common occupations requiring design thinking skills .

Since engineers are often responsible for solving complex problems, it’s easy to get lost in the details and set creative problem-solving skills aside. Creativity in business is beneficial because it:

  • Encourages innovation
  • Boosts productivity
  • Allows for adaptability
  • Fosters growth

Graphic listing the benefits of creativity in business

Leveraging design thinking skills to pursue innovation not only helps professionals find creative solutions but identify business opportunities , evaluate market needs , and design new products and services.

Engineers’ responsibilities can vary. Whether creating new products or maintaining existing ones, engineering revolves around design . For this reason, a systematic approach is highly valuable when encountering industry challenges.

7 Engineering Challenges Design Thinking Can Solve

Some of the challenges engineers often face include:

  • Identifying obscure problems
  • Overcoming cognitive fixedness
  • Designing sustainable innovations
  • Addressing the skilled labor shortage
  • Encouraging diversity
  • Keeping up with advancing technology
  • Overcoming status-quo bias

Here’s an overview of how design thinking can help solve these problems.

1. Identifying Obscure Problems

Engineers often encounter problems that are difficult to identify. As a result, it can be easy for them to jump to conclusions based on preexisting knowledge of a design or situation. Datar discourages this in Design Thinking and Innovation .

"Whenever you have a difficult problem, you tend to solve the fringes of it,” Datar says. “But try and go for the most important part that you need to solve."

For example, if you're trying to remove a major obstacle preventing a project’s completion, you might be tempted to search for a cause equal in scope to its impact. However, some of the biggest design problems can be caused by something as simple as a misplaced hyphen or a loose screw. Often, the best approach is to consider the bigger picture. Is there anything in the design you don't understand?

The clarification stage in the design thinking framework encourages you to obtain insights through unbiased observation. An effective tool to accomplish this is journey mapping , which involves creating a chronological visual timeline of everything you know about a problem.

According to Design Thinking and Innovation , the three steps to developing a journey map are:

  • Creating observations about the user's journey
  • Writing those observations on a timeline
  • Organizing the observations into different stages

Creating a timeline of events can help identify when a problem occurs, as well as what precedes and follows it. This can enable you to narrow down its cause.

2. Overcoming Cognitive Fixedness

Cognitive fixedness is a mindset that assumes there's just one way to accomplish tasks. It considers every situation through the lens of past decisions. Thinking "if it worked in the past, it'll work now" is easy to follow, especially in the engineering industry, where replicating past successes is often the best way to proceed.

For example, while new technology trends can succeed in the market because of their innovative features, incorporating those features into an existing design might not be feasible—and even prevent you from meeting critical deadlines. Furthermore, in areas with high risk to human life—such as submarine design—it may be advisable to incorporate technology that’s proven effective before creating something new.

While caution is important, cognitive fixedness can prevent innovation, resulting in obsolescence. You must strike a balance between the operational and the innovation worlds.

The difference between the two worlds is described in Design Thinking and Innovation :

  • The operational world represents a business’s routine procedures.
  • The innovation world facilitates open-endedly exploring ideas.

Although the operational world is important, it can result in cognitive fixedness and prevent ideas’ progression. If you're struggling to overcome cognitive fixedness—whether your own or someone else's—consider why there's an unwillingness to change to determine the next steps.

3. Designing Sustainable Innovations

Climate change is a pressing issue impacting businesses around the globe . An increasing number of organizational leaders are addressing it by focusing on the triple bottom line . According to the HBS Online course Sustainable Business Strategy , the triple bottom line considers:

  • Profit: Satisfying shareholders and producing a profit
  • People: Impacting society in a positive, measurable way
  • The planet: Making a positive impact on the environment

By reframing problems and pursuing workable solutions that don't sacrifice profit, you can effectively incorporate sustainability into business strategies .

Design Thinking and Innovation | Uncover creative solutions to your business problems | Learn More

4. Addressing the Skilled Labor Shortage

The United States is experiencing a shortage of engineers , which has put a strain on employers hoping to hire qualified candidates in a shrinking market.

Consider how you'd approach this challenge from a design thinking perspective. Clarifying the problem might highlight opportunities you didn't previously think of. For instance, companies such as Google and Microsoft have invested in science, technology, engineering, and math (STEM) education , enabling more people to pursue careers in those industries.

Other companies have sought ways to attract engineering talent. It can be easy to draw candidates by raising salaries or increasing benefits, but many engineers aren't comfortable working for organizations that harm the environment. Your firm should consider adopting a sustainable business strategy that could benefit the planet and attract qualified applicants.

5. Encouraging Diversity

Engineering has historically been a male-dominated field. One of the primary causes of this imbalance is the workplace stereotype that STEM careers are masculine. This has resulted in implicit—and often direct—discouragement of women from pursuing STEM careers.

In the context of design thinking, clarifying and reframing the problem might result in questions like, "How can we empower more women to pursue STEM careers?"

Through exploring potential solutions, you may discover that encouraging and empowering a diverse population to pursue engineering can help address other challenges, such as the skilled labor shortage.

6. Keeping Up with Advancing Technology

Technology is continuously advancing; companies that fail to adapt might get left behind. For example, Blackberry was once one of the fastest-growing smartphone companies in the world. Yet, its products became obsolete when the company refused to adopt touch-screen technology. This resulted in Blackberry losing 90 percent of its market share between 2009 and 2013.

Design thinking encourages continual awareness to avoid these downward trends. Learning how to recognize opportunities and communicate them to others can prevent a business from falling behind.

7. Overcoming Status-Quo Bias

Resistance to change doesn't just occur within an organization—it happens among customers, too. This is known as status-quo bias , which is a challenge you must address during implementation.

The challenge is how to retain existing customers while appealing to the current market and acquiring new ones. Avoid assuming users will understand a design change you’ve implemented just because it makes sense to you.

According to Datar in Design Thinking and Innovation , you should consider three views during the implementation phase:

  • The developer's view: The designer with knowledge and understanding of a design's utility and benefits
  • The neutral view: Someone who doesn't have a preexisting opinion about the design
  • Stakeholders' view: Existing customers and users who have existing opinions based on the status quo

Learning how to overcome status-quo bias is critical to successful innovation.

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Improving Your Design Thinking Skills

Whether encountering one of the engineering challenges mentioned above or something more niche, design thinking can be a valuable tool for solving them.

Learning about the process and its business applications can enable you to climb the corporate ladder and make an impact on your organization.

Ready to learn the tools you need to innovate? Enroll in our online certificate course Design Thinking and Innovation —one of our entrepreneurship and innovation courses —and develop in-demand skills that can benefit your engineering career. If you aren’t sure which HBS Online course is right for you, download our free flowchart to explore your options.

how to solve an engineering problem

Methods to Solve Any Engineering Problem

In our day to day life we came across various engineering problems. Once we face these engineering problems few questions will come in our mind like How to resolve it? What are different methods?  Which is the simplest or best method? 

In this paragraphs, we will discuss various methods to solve any engineering problems & their comparison with each other. There are three basic methods to solve any engineering methods.

  • Analytical Methods
  • Numerical Methods
  • Experimental methods

1. Analytical Methods:  

The analytical method is most widely used in curriculum study as well as used by industrial designers to solve the engineering problems. It is a classical approach which gives 100 % accurate results. This approach is also referred to as hand calculations; as in this method various mathematical equations & functions are used to find output variables & derive closed form solutions. This method is mainly applicable for simpler problems like cantilever and simply supported fixed beams, etc. 

Though the analytical approach is 100 % accurate, it could also give approximate results if the solution is not closed form. An equation is said to be a closed-form solution if it solves a given problem in terms of mathematical operations & functions from a given generally accepted set. For example, an infinite sum would generally not be considered closed-form.

2. Numerical Method:

When we come across more complex problems, in which both analytical and experimental methods do not work, numerical methods are driving the solutions. CAE engineers or analysts most widely use numerical methods to solve their engineering problems. This numerical method uses computational techniques through simulation software’s & large infrastructures, etc. Numerical methods do not need physical models or prototypes, it builds mathematical models to replicate real life complex problems and while doing so, several assumptions were made to simulate the analysis. Therefore, the results from this method are approximate. So, you cannot believe the results blindly and hence, sometimes sanity checks are needed to validate the simulation either by hand calculations or by physical testing, etc.

The four common numerical methods used to solve engineering problems are:

  • The Finite Element Method (FEM) is a popular numerical technique used to determine the approximated solution for a partial differential equation (PDE). 
  • Applications : Linear, nonlinear, buckling, thermal, dynamic, and fatigue analysis
  • Powerful and efficient technique to solve acoustics or NVH problems.  Just like FEA, it also requires nodes and elements, but it only considers the outer boundary of the domain. So when the problem is of a volume, only the outer surfaces are considered. Similarly if the domain is of an area, then only the outer periphery is considered. By doing so it reduces the dimensionality of the problems by one degree resulting in faster problem solving. BEM is often more efficient than other methods in terms of computational resources for problems where there is a small surface or volume ratio. 
  • Applications : Acoustics, NVH
  • The FVM method representing and evaluating partial differential equations as an algebraic equations method is used in many computational fluid dynamics packages. It is very similar to FDM, where the values are calculated at discrete volumes on a generic geometry. The advantage of this method is that it is easily formulated to allow for unstructured meshes.
  • Applications : CFD (Computational Fluid Dynamics) and Computational Electromagnetic
  • It uses Taylor’s series to convert a differential equation to an algebraic equation. In the conversion process, higher order terms are neglected. 
  • It is used in combination with BEM or FVM to solve thermal and CFD coupled problems.
Can we solve the same problem with all Numerical methods? The answer is YES, but substantial differences exist between this method in terms of accuracy, ease of programming & computational time, etc.

3. Experimental Method:

Experimental method is also known as physical testing. It is one of the most reliable methods and widely used in industry for product prototype testing.

In this method, the product or component is tested in real time operating conditions & actual measurement were reported. So in order to use this method, you will need a physical prototype of the product or structure you want to be analyzed. Only one prototype testing is not sufficient, for final outcome of analysis 3 to 5 prototype testing is required. Due to this, the experimental method is time consuming, requires expensive physical setup which results in additional cost rather than actual products.  

Physical testing is performed with the help of various measuring equipment like strain gauges, different sensors, measuring devices like accelerators, etc. to calculate various parameters of the experiment. Examples: Compressor manufacturers are doing prototype testing to mitigate the vibration levels on prototypes. Here, different accelerators are placed at various point on prototype and acceleration levels are measured for operational loads.

Hydraulic Material testing Machine

Below images shows the simple cantilever beam problems solution by three different methods approach.

Analytical Method

UNIT 1: How to Think Like an Engineer.

Learning objectives.

  • Explain what we mean by “Computational Thinking”.
  • Describe the problem being solved in a computational algorithm.
  • Explain the process for generating computational algorithms.
  • Generate and test algorithms to solve computational problems.
  • Evaluate computational algorithms for exactness, correctness, termination, generalizability and understandability.
  • Explain the role of programming in the field of Informatics.


The goal of this book is to teach you to solve computational problems and to think like an engineer. Computational problems are problems that can be solved by the use of computations (a computation is what you do when you calculate something). Engineers are people who solve problems – they invent, design, analyze, build and test “things” to fulfill objectives and requirements. The single most important skill for you to learn is problem solving. Problem solving means the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills.

This book strives to prepare you to write well-designed computer programs that solve interesting problems involving data.

Computational Thinking


Figure 1: “The seven components to computational thinking”(www.ignitemyfutureinschool.org/about)

Computational Thinking is the thought processes involved in understanding a problem and expressing its solution in a way that a computer can effectively carry out. Computational thinking involves solving problems, designing systems, and understanding human behavior (e.g. what the user needs or wants) – thinking like an engineer. Computational thinking is a fundamental skill for everyone, not just for programmers because computational thinking is what comes before any computing technology. [1]

Computer science is the study of computation — what can be computed and how to compute it whereas computational thinking is:

Conceptualizing , not programming. Computer science is not only computer programming. Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction;

Fundamental , not rote skill. A fundamental skill is something every human being must know to function in modern society. Rote means a mechanical routine;

A way that humans, not computers, think . Computational thinking is a way humans solve problems; it is not trying to get humans to think like computers. Computers are dull and boring; humans are clever and imaginative. We humans make computers exciting. Equipped with computing devices, we use our cleverness to tackle problems we would not dare take on before the age of computing and build systems with functionality limited only by our imaginations;

Complements and combines mathematical and engineering thinking . Computer science inherently draws on mathematical thinking, given that, like all sciences, its formal foundations rest on mathematics. Computer science inherently draws on engineering thinking, given that we build systems that interact with the real world;

Ideas , not artifacts. It’s not just the software and hardware artifacts we produce that will be physically present everywhere and touch our lives all the time, it will be the computational concepts we use to approach and solve problems, manage our daily lives, and communicate and interact with other people;

For everyone, everywhere . Computational thinking will be a reality when it is so integral to human endeavors it disappears as an explicit philosophy. [2]

how to solve an engineering problem

Figure 2 “Are you happy?” by Typcut http://www.typcut.com/headup/are-you-happy

An algorithm specifies a series of steps that perform a particular computation or task. Throughout this book we’ll examine a number of different algorithms to solve a variety of computational problems.

Algorithms resemble recipes. Recipes tell you how to accomplish a task by performing a number of steps. For example, to bake a cake the steps are: preheat the oven; mix flour, sugar, and eggs thoroughly; pour into a baking pan; set the timer and bake until done.

However, “algorithm” is a technical term with a more specific meaning than “recipe”, and calling something an algorithm means that the following properties are all true:

  • An algorithm is an unambiguous description that makes clear what has to be implemented in order to solve the problem. In a recipe, a step such as “Bake until done” is ambiguous because it doesn’t explain what “done” means. A more explicit description such as “Bake until the cheese begins to bubble” is better. In a computational algorithm, a step such as “Choose a large number” is vague: what is large? 1 million, 1 billion, or 100? Does the number have to be different each time, or can the same number be used again?
  • An algorithm expects a defined set of inputs. For example, it might require two numbers where both numbers are greater than zero. Or it might require a word, or a list customer names.
  • An algorithm produces a defined set of outputs. It might output the larger of the two numbers, an all-uppercase version of a word, or a sorted version of the list of names.
  • An algorithm is guaranteed to terminate and produce a result, always stopping after a finite time. If an algorithm could potentially run forever, it wouldn’t be very useful because you might never get an answer.
  • Must be general for any input it is given. Algorithms solve general problems (determine if a password is valid); they are of little use if they only solve a specific problem (determine if ‘comp15’ is a valid password)
  • It is at the right level of detail…..the person or device executing the instruction know how to accomplish the instruction without any extra information.

Once we know it’s possible to solve a problem with an algorithm, a natural question is whether the algorithm is the best possible one. Can the problem be solved more quickly or efficiently?

The first thing you need to do before designing an algorithm is to understand completely the problem given. Read the problem’s description carefully, then read it again. Try sketching out by hand some examples of how the problem can be solved. Finally consider any special cases and design your algorithm to address them.

An algorithm does not solve a problem rather it gives you a series of steps that, if executed correctly, will result in a solution to a problem.

An Example Algorithm

Let us look at a very simple algorithm called find_max.

Problem : Given a list of positive numbers, return the largest number on the list.

Inputs : A list of positive numbers. This list must contain at least one number. (Asking for the largest number in a list of no numbers is not a meaningful question.)

Outputs : A number, which will be the largest number in the list.

Algorithm :

  • Accept a list of positive numbers; set to nums_list
  • Set max_number to 0.
  • If the number is larger, set max_number to the larger number.
  • max_number is now set to the largest number in the list of positive numbers, nums_list.

Does this meet the criteria for being an algorithm?

  • Is it unambiguous? Yes. Each step of the algorithm consists of uncomplicated operations, and translating each step into programming code is straight forward.
  • Does it have defined inputs and outputs? Yes.
  • Is it guaranteed to terminate? Yes. The list nums_list is of finite length, so after looking at every element of the list the algorithm will stop.
  • Is it general for any input? Yes. A list of any set of positive numbers works.
  • Does it produce the correct result? Yes. When tested, the results are what are expected

[3] Figure 3: Example Algotithm

Verifying your Algorithm

How do we know if an algorithm is unambiguous, correct, comes to an end, is general AND is at the right level of detail? We must test the algorithm. Testing means verifying that the algorithm does what we expect it to do. In our ‘bake a cake’ example we know our algorithm is ‘working’ if, in the end, we get something that looks, smells and tastes like a cake.

how to solve an engineering problem

Figure 4 “ Keyboard ” by Geralt is licensed under CC 2

Your first step should be to carefully read through EACH step of the algorithm to check for ambiguity and if there is any information missing. To ensure that the algorithm is correct, terminates and is general for any input we devise ‘test cases’ for the algorithm.

A test case is a set of inputs, conditions, and expected results developed for a particular computational problem to be solved. A test case is really just a question that you ask of the algorithm (e.g. if my list is the three numbers 2, 14, and 11 does the algorithm return the number 14?). The point of executing the test is to make sure the algorithm is correct, that it terminates and is general for any input.

Good (effective) test cases:

  • are easy to understand and execute
  • are created with the user in mind (what input mistakes will be made? what are the preconditions?)
  • make no assumptions (you already know what it is supposed to do)
  • consider the boundaries for a specified range of values.

Let us look at the example algorithm from the previous section. The input for the algorithm is ‘a list of positive numbers’. To make it easy to understand and execute keep the test lists short. The preconditions are that the list only contains numbers and these numbers must be positive so include a test with a ‘non-number’ (i.e. a special character or a letter) and a test with a negative number. The boundaries for the list are zero and the highest positive number so include a test with zero and a large positive number. That is it! Here is an example of three different test cases.

Manually, you should step through your algorithm using each of the three test cases, making sure that the algorithm does indeed terminate and that you get your expected result. As our algorithms and programs become more complex, skilled programmers often break each test case into individual steps of the algorithm/program and indicate what the expected result of each step should be. When you write a detailed test case, you don’t necessarily need to specify the expected result for each test step if the result is obvious.

In computer programming we accept a problem to solve and develop an algorithm that can serve as a general solution. Once we have such a solution, we can use our computer to automate the execution. Programming is a skill that allows a competent programmer to take an algorithm and represent it in a notation (a program) that can be followed by a computer. These programs are written in programming languages (such as Python). Writing a correct and valid algorithm to solve a computational problem is key to writing good code. Learn to Think First and coding will come naturally!

Computational problem solving does not simply involve the act of computer programming. It is a process, with programming being only one of the steps. Before a program is written, a design for the program must be developed (the algorithm). And before a design can be developed, the problem to be solved must be well understood. Once written, the program must be thoroughly tested. These steps are outlined in Figure 5.

how to solve an engineering problem

Figure 5: Process of Computational Problem Solving

Values and Variables

A value is one of the basic things computer programs works with, like a password or a number of errors.

Values belong to different types: 21 is an integer (like the number of errors), and ‘comp15’ is a string of characters (like the password). Python lets you give names to values giving us the ability to generalize our algorithms.

One of the most powerful features of a programming language is the ability to use variables. A variable is simply a name that refers to a value as shown below,

Whenever the variable errors appears in a calculation the current value of the variable is used.

We need some way of storing information (i.e. the number of errors or the password) and manipulate them as well. This is where variables come into the picture. Variables are exactly what the name implies – their value can vary, i.e., you can store anything using a variable. Variables are just parts of your computer’s memory where you store some information. Unlike literal constants, you need some method of accessing these variables and hence you give them names.

Programmers generally choose names for their variables that are meaningful and document what the variable is used for. It is a good idea to begin variable names with a lowercase letter . The underscore character (_) can appear in a name and is often used in names with multiple words.

What is a program?


Figure 6: “ Python Code ” by nyuhuhuu is licensed under CC-BY 2.0

A program is a sequence of instructions that specifies how to perform a computation. The computation might be something mathematical, such as solving a system of mathematical equations or finding the roots of a polynomial, but it can also be a symbolic computation, such as searching and replacing text in a document or something graphical, like processing user input on an ATM device.

The details look different in different computer programming languages, but there are some low-level conceptual patterns (constructs) that we use to write all programs. These constructs are not just for Python programs, they are a part of every programming language.

input Get data from the “outside world”. This might be reading data from a file, or even some kind of sensor like a microphone or GPS. In our initial algorithms and programs, our input will come from the user typing data on the keyboard.

output Display the results of the program on a screen or store them in a file or perhaps write them to a device like a speaker to play music or speak text.

sequential execution Perform statements one after another in the order they are encountered in the script.

conditional execution Checks for certain conditions and then executes or skips a sequence of statements.

repeated execution Perform some set of statements repeatedly, usually with some variation.

reuse Write a set of instructions once and give them a name and then reuse those instructions as needed throughout your program.

Believe it or not, that’s pretty much all there is to it. Every computer application you’ve ever used, no matter how complicated, is made up of constructs that look pretty much like these. So you can think of programming as the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed with one of these basic constructs. The “art” of writing a program is composing and weaving these basic elements together many times over to produce something that is useful to its users.

Computational Problem Design using the Basic Programming Constructs

The key to better algorithm design and thus to programming lies in limiting the control structure to only three constructs as shown below.

  • The Sequence structure (sequential execution)
  • The Decision, Selection or Control structure (conditional execution)
  • Repetition or Iteration Structure (repeated execution)


Figure 7: the 3 Programming Constructs

  Let us look at some examples for the sequential control and the selection control.

Sequential Control Example

The following algorithm is an example of sequential control .

Problem : Given two numbers, return the sum and the product of the two numbers.

Inputs : Two numbers.

Outputs : The sum and the product.

  • display “Input two numbers”
  • accept number1, accept number2
  • sum = number1 + number2
  • print “The sum is “, sum
  • product = number1 * number2
  • print “The product is “, product
  • Is it guaranteed to terminate? Yes. Sequential control, by its nature, always ends.
  • Is it general for any input? Yes. Any two numbers work in this design.
  • Does it produce the correct result? Yes. When tested, the results are what are expected.

Here is an example of three different test cases that are used to verify the algorithm.

Selection Control Examples

The following two algorithms are examples of selection control which uses the ‘IF’ statement in most programming languages.

Problem : Given two numbers, the user chooses to either multiply, add or subtract the two numbers. Return the value of the chosen calculation.

Inputs : Two numbers and calculation option.

Outputs : The value of the chosen calculation.

The relational (or comparison) operators used in selection control are:

= is equal to [in Python the operator is ==]

> is greater than

< is less than

>= is greater than or equal

<= is less than or equal

<> is not equal to [in Python the operator is !=]

  • display “choose one of the following”
  • display “m for multiply”
  • display “a for add”
  • display “s for subtract”
  • accept choice
  • display “input two numbers you want to use”
  • accept number1, number2
  • if choice = m then answer= number1 * number2
  • if choice = a then answer= number1 + number2
  • if choice = s then answer= number1 -number212. if choice is not m, a, or s then answer is NONE
  • display answer
  • Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s choice and the two numbers the algorithm will stop.
  • Is it general for any input? Yes. Any two numbers work in this design and only a choice of a’m’, ‘a’, or ‘s’ will result in numeric output.

This example uses an extension of the simple selection control structure we just saw and is referred to as the ‘IF-ELSE’ structure.

Problem : Accept from the user a positive integer value representing a salary amount, return tax due based on the salary amount.

Inputs : One positive integer number.

Outputs : The calculated tax amount.

= is equal to  [in Python the operator is ==]

<> is not equal to  [in Python the operator is !=]

  • accept salary
  • If salary < 50000 then
  • Tax = 0 Else
  • If salary > 50000 AND salary < 100000 then
  • Tax = 50000 * 0.05 Else
  • Tax = 100000 * 0.30
  • display Tax
  • Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s number, even if it is negative, the algorithm will stop.
  • Is it general for any input? Yes. Any number entered in this design will work.

Iterative Control Examples

The third programming control is the iterative or, also referred to as, the repetition structure. This control structure causes certain steps to be repeated in a sequence a specified number of times or until a condition is met. This is what is called a ‘loop’ in programming

In all programming languages there are generally two options: an indefinite loop (the Python ‘WHILE’ programming statement) and a definite loop (the Python ‘FOR’ programming statement). We can use these two constructs, WHILE and FOR, for iterations or loops in our algorithms.

Note for Reader: A definite loop is where we know exactly the number of times the loop’s body will be executed. Definite iteration is usually best coded as a Python for loop. An indefinite loop is where we do not know before entering the body of the loop the exact number of iterations the loop will perform. The loop just keeps going until some condition is met. A while statement is used in this case.

The following algorithm is an example of iterative control using WHILE .

Problem : Print each keyboard character the users types in until the user chooses the ‘q’ (for ‘quit’) character.

Inputs : A series of individual characters.

Outputs : Each character typed in by the user.

  • initialize (set) letter = ‘a’
  • WHILE letter <> ‘q’
  • ACCEPT letter
  • DISPLAY “The character you typed is”, letter
  • Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s keyboard character, even if it is not a letter, the algorithm will stop.
  • Is it general for any input? Yes. Any keyboard character entered in this design will work.

The following algorithm is an example of iterative control using FOR . This statement is used when the number of iterations is known in advance.

Problem : Ask the user how many words they want to enter then print the words entered by the user.

Inputs : Number of words to be entered; this value must be a positive integer greater than zero. Individual words.

Outputs : Each word typed in by the user.

  • accept num_words (must be at least one)
  • repeat num_words times (FOR 1 to num_words)
  • accept word
  • DISPLAY “The word you entered is”, word
  • Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s number of words to enter and any characters typed on the keyboard, even if it is not a ‘word’ per say, the algorithm will stop.
  • Is it general for any input? Yes. Any positive integer greater than zero and any size ‘word’ will work.

Here is an example of two different test cases that are used to verify the algorithm.

The Role of Programming in the Field of Informatics


Figure8: iPhone apps by Jaap Arriens/NurPhoto via Getty Images (abcnews.go.com)

You see computer programming in use every day. When you use Google or your smartphone, or watch a movie with special effects, there is programing at work. When you order a product over the Internet, there is code in the web site, in the cryptography used to keep your credit card number secure, and in the way that UPS routes their delivery vehicle to get your order to you as quickly as possible.

Programming is indeed important to an informatics professional as they are interested in finding solutions for a wide variety of computational problems involving data.

When you Google the words “pie recipe,” Google reports that it finds approximately 38 million pages, ranked in order of estimated relevance and usefulness. Facebook has approximately 1 billion active users who generate over 3 billion comments and “Likes” each day. GenBank, a national database of DNA sequences used by biologists and medical researchers studying genetic diseases, has over 100 million genetic sequences with over 100 billion DNA base pairs. According to the International Data Corporation, by 2020 the digital universe – the data we create and copy annually – will reach 44 zettabytes, or 44 trillion gigabytes.


Figure 9: The Digital Universe ( www.emc.com/leadership/digital-universe/2014iview/images )

  Doing meaningful things with data is challenging, even if we’re not dealing with millions or billions of things. In this book, we will be working with smaller sets of data. But much of what we’ll do will be applicable to very large amounts of data too.

Unit Summary

Computational Thinking is the thought processes involved in formulating a problem and expressing its solution in a way that a computer—human or machine—can effectively carry out.

Computational Thinking is what comes before any computing technology—thought of by a human, knowing full well the power of automation.

Writing a correct and valid algorithm to solve a computational problem is key to writing good code.

  • What are the inputs?
  • What are the outputs (or results)?
  • Can we break the problem into parts?
  • Think about the connections between the input & output.
  • Consider designing ‘backwards’.
  • Have you seen the problem before? In a slightly different form?
  • Can you solve part of the problem?
  • Did you use all the inputs?
  • Can you test it on a variety of inputs?
  • Can you think of how you might write the algorithm differently if you had to start again?
  • Does it solve the problem? Does it meet all the requirements? Is the output correct?
  • Does it terminate?
  • Is it general for all cases?

Practice Problems

  • Write about a process in your life (e.g. driving to the mall, walking to class, etc.) and estimate the number of steps necessary to complete the task. Would you consider this a complex or simple task? What happens if you scale that task (e.g. driving two states away to the mall)? Is your method the most efficient? Can you come up with a more efficient way?


  • Write an algorithm to find the average of 25 test grades out of a possible 100 points.
  • If you are given three sticks, you may or may not be able to arrange them in a triangle. For example, if one of the sticks is 12 inches long and the other two are one inch long, it is clear that you will not be able to get the short sticks to meet in the middle. For any three lengths, there is a simple test to see if it is possible to form a triangle: “If any of the three lengths is greater than the sum of the other two, then you cannot form a triangle. Otherwise, you can.”Write an algorithm that accepts three integers as arguments, and that displays either “Yes” or “No,” depending on whether you can or cannot form a triangle from sticks with the given lengths.
  • ROT13 is a weak form of encryption that involves “rotating” each letter in a word by 13 places. To rotate a letter means to shift it through the alphabet, wrapping around to the beginning if necessary, so ‘A’ shifted by 3 is ‘D’ and ‘Z’ shifted by 1 is ‘A’. Write an algorithm that accepts a word and an integer from the user, and that prints a new encrypted word that contains the letters from the original word “rotated” by the given amount (the integer input). For example, “cheer” rotated by 7 is “jolly” and “melon” rotated by −10 is “cubed.”
  • Write an algorithm which repeatedly accepts numbers until the user enters “done”. Once “done” is entered, display the total sum of all the numbers, the count of numbers entered, and the average of all the numbers.
  • Write an algorithm that sums a series of ten positive integers entered by the user excluding all numbers greater than 100. Display the final sum.
  • Wing, Jeannette M. "Computational thinking." Communications of the ACM 49.3 (2006): 33-35. ↵

how to solve an engineering problem

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How to Solve Any Problem in Engineering in Three Basic Steps

  • by Dee Reyes
  • September 10, 2021 September 13, 2021

how to solve an engineering problem

An engineering student is always bombarded with numerical and worded problems that need step-by-step solutions to arrive to the answers. Solving these problems enable learning of the subject matter at hand with an aim to apply the principles in real life. After all, that’s what engineering is for.

But how does one approach a problem correctly? Just follow these three basic steps:

State the given.

Particularly for worded problems, the first critical step in solving any engineering problem is to gather the given information and known quantities.

There will be cases that your professor will feed you with values you don’t need to confuse or test your ability to separate what is needed in the problem. But sometimes, there are values that are not provided like the value of g or pi which are also essential. It has to be made sure as well that all the values belong to the same system of units, like in measurements feet versus meter, kilogram versus pound, so convert the values right away as necessary to avoid confusion later.

Moreover, do not forget the so-called boundary conditions, or constraints that apply to the problem.

Find the required.

The problem usually states explicitly what it is looking for, so focus on that. It is recommended to assign a symbol for the unknown.

Write it so you would not forget including the unit. It’s just like setting a goal that you need to arrive to.

Show the solution.

It sounds simple, but a solution is more than just a computation – it needs to have first a free body diagram (FBD), or a sketch complete with labels to be able to visualize the variables in aid of interpreting the problem.

Even if it is not needed, as the one who solves the problem it might give you a better understanding of the given values. Name and label the parts of the sketch accordingly.

Based on the FBD, the next questions you need to ask yourself are the following, not necessarily in particular order:

  • What principles or formulas are to be applied in this problem?
  • What could be the underlying assumptions or conditions?
  • Is there only one way to interpret the problem or one way to solve it?
  • Can the sketch be simplified further?

Once everything has been settled and simplified, do the math algebraically then numerically with the calculator. It pays to be careful to press the right buttons, so at this point there is no reason to make a mistake if you are doing the correct math.

You can perform several computations with your mind having the confidence with your arithmetic, but then this could be prone to human error. Each level of the equation should be written to avoid this and even the most basic 3×3 is to be done in a calculator to make sure it is the correct answer 9.

To complete the solution, box the final answer for it to be identified right away, which should be in line with the “required” item previously defined. In some cases, it might need to be presented in graph or tables.

But before submission, double check each step of the solution. Always.

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How Engineers Effectively do Problem-solve and Troubleshoot?

The basic fundamentals and practical problem-solving skills required for the engineers to effectively troubleshoot the issue in the industries.

Table of Contents

Engineers Problem-solve and Troubleshoot

How Engineers Effectively do Problem-solve and Troubleshoot

Rely on principles, not procedures.

Don’t be satisfied with memorizing steps – learn why those steps work. Each step should make logical sense and have real-world meaning to you.

Sketch a diagram

Sketch a diagram to help visualize the problem. Sketch a graph showing how variables relate. When building a real system, always prototype it on paper and analyze its function before constructing it.

Identify what it is you need to solve, identify all relevant data, identify all units of measurement , identify any general principles or formulae linking the given information to the solution, and then identify any “missing pieces” to a solution. Annotate all diagrams with this data.

Perform “thought experiments”

Perform “thought experiments” to explore the effects of different conditions for theoretical problems. When troubleshooting, perform diagnostic tests rather than just visually inspect for faults.

Simplify the Problem

Simplify the problem and solve that simplified problem to identify strategies applicable to the original problem (e.g. change quantitative to qualitative, or visa-versa; substitute easier numerical values; eliminate confusing details; add details to eliminate unknowns; consider simple limiting cases; apply an analogy). Remove components from a malfunctioning system to simplify it and better identify the nature and location of the problem.

Check for Exceptions

Check for exceptions – does your solution work for all conditions and criteria?

Work backward

Work “backward” from a hypothetical solution to a new set of given conditions.

General follow-up challenges for assigned problems

Identify where any fundamental laws or principles apply to the solution of the problem.

Analyze the details in your own strategy for solving the problem. How did you identify and organized the given information? Did you sketch any diagrams to help frame the problem?

Is there more than one way to solve the problem? Which method seems best to you?

Analyze the work you did in solving the problem, even if the solution is incomplete or incorrect.

What would you say was the most challenging part of the problem, and why was it so?

Was any important information missing from the problem which you had to research or recall?

Was there any extraneous information presented within the problem? If so, what was it and why did it not matter?

Examine someone else’s solution (previous or similar) to identify where they applied fundamental laws or principles.

Simplify the problem from its given form and show how to solve this simpler version of it. Examples include eliminating certain variables or conditions, altering values to simpler (usually whole) numbers, applying a limiting case (i.e. altering a variable to some extreme or ultimate value).

For quantitative problems, identify the real-world meaning of all intermediate calculations: their units of measurement, where they fit into the scenario at hand.

For quantitative problems, try approaching it qualitatively instead, thinking in terms of “increase” and “decrease” rather than definite values.

For qualitative problems, try approaching it quantitatively instead, proposing simple numerical values for the variables.

Were there any assumptions you made while solving this problem? Would your solution change if one of those assumptions were altered?

Identify where it would be easy for someone to go astray in attempting to solve the problem.

Formulate your own problem based on what you learned solving this one.

Share Your Experiences, Principles, Problem-solving skills with us through comments.

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An engineering company needs to solve a design problem. It is designing a high-speed train to transport passengers between Boston and Atlanta. Which statement is a criterion for this project? O A. The train must not take more than six years to build B. The train must not have wheels with bearings that need lubrication, O C. The train must cost less than $150 million to design. D. The train must be able to maintain a speed of 250 km/h.


Answer:D.the train must be able to maintain a speed of 250km/h.


📚 Related Questions

Why is it impossible for an element to have an atomic number of 110.5? a. atoms of an element have the same whole number of protons and neutrons b. atoms of an element all have the same whole number of protons c. exactly half of the isotopes would need an atomic number of 110 and half would need an atomic number of 111 which is very unlikely d. atoms with atomic numbers greater than 100 are unstable

Explanation: The atomic number is based only on the number of protons in the nucleus of an atom. Since this is a count of whole numbers, it cannot be a decimal. It's either element 110 or 111, not 110.5.

These should be the answers for your test. If you have any questions, please DM me

PLEASE HELP WITH MARK BRAINLIEST !! Which of these is a special property of water? select all that apply water has a high surface tension none water expands when it freezes water molecules can stick together

Water has high surface tension, and water molecules stick together

Answer: C and D

Explanation: Please give brainlyest

The only type of movement particles in a solid do is

:small vibrational movements.

The particles of a solid are not able to move out of their positions relative to one another, but do have small vibrational movements.



Jupiter's moon Europa orbits the planet at a distance of about 671,030 km. What is the correct way to write this distance in scientific notation? A. 67.103 x 10-4 km B. 67.103 x 104 km C. 6.7103 x 105 km D. 6.7103 x 10-5 km​

Answer:6.7103x10^5 km

The planet is at a distance of about 6.71030 ×10⁵ km . Therefore, option (c) is correct.

What is scientific notation?

Scientific notation is a way of representing a quantity as a number having significant digits that are necessary for a s pecified degree and multiplied by ten to the power.

The general form of scientific notation can be written as [tex]N \times 10^{a}[/tex] .

A significant digit is that digit in a number which adds to its precision. A significant includes all nonzero numbers , zeros between significant digits, and zeros represent to be significant while leading and trailing zeros are not significant digits as they exist only to represent the scale of number.

Given, using the scientific notation method we can write the scientific notation of the distance of 671,030 km.

The number 671,030 km can also be written as 6.71030 ×10⁵ km.

Therefore, the correct way to write this distance in the scientific notation of  671,030 km is 6.71030 ×10⁵ km.

Learn more about scientific notation , here:


Details : Jupiter's moon Europa orbits the planet at a distance of about 671,030

ANY HELP??? it’s due today

Choose the 3rd option: methane, ozone, and carbon.

methane and carbon dioxide

in eukaryotes, which rna polymerase is responsible for transcribing mrnas?

how is the reactivity of a metal summarized in the activity series? how does the placement of a metal in the activity series allow you to predict whether a reaction will, or will not, occur?

The metal with higher reactivity is placed on the top of the series .

  • A reactivity series of metals is a list of metals ranging from highly reactive metal to least reactive metal .
  • The highly reactive metals are on the top of the list and as we move down the series reactivity of metal decreases.
  • Metal being placed above another metal indicates that the former will easily replace the latter from its compound.
  • Metals on top have the highest tendency to lose electrons and form a positive ion.
  • If the metal of lower reactivity is added to the aqueous solution of metal with higher reactivity then no reaction will be observed .
  • If the metal of higher reactivity is added to the aqueous solution of metal with lower reactivity then the reaction will be observed .

So, from this, we can conclude that the metal with higher reactivity is placed on the top of the series.

Learn more about the reactivity series of metal here:



can an element be broken down into simpler substances

Note that an element: consists of only one kind of atom, cannot be broken down into a simpler type of matter by either physical or chemical means, and. can exist as either atoms (e.g. argon) or molecules (e.g., nitrogen).

Details : can an element be broken down into simpler substances

Whoever answers it correctly will get Brainly

I think 2 and 3 possibly!

Define deposition in your own word∧∧∨∨

develop a hypothesis that could explain why a soap created from the acid ch3ch2ch2ch2cooh has poorer cleaning properties than soap made from palmitic acid.

Below is a theory that may explain why such a soap manufactured from the acid does have lower cleaning capabilities than just a component (soap) manufactured from palmitic acid .

  • Because valeric acid seems to have the chemical formula C5H10O2 whereas palmitic acid does have the composition C15H32O2 .
  • This implies that throughout the instance of palmitic acid , there'll be a continuous stream of hydrophobic compounds , which would also improve the cleaning characteristic by detaching waste from garments, although in the context of valeric acid, the above would be far less.

Learn more about Palmitic acid here:


what is the formula for dry ice

Dry ice is solid carbon dioxide, with the formula CO₂.

Details : what is the formula for dry ice

Convert 1345 g to mg ​

multiply the mass value by 1000

What is the weight in grams of 3.36 × 1023 molecules of copper sulfate (CuSO4)?

(3.36x10^23 molecules ÷ 6.02x10^23 molecules)(159.62 g/mol) = 89.1 g

What volume would a 200.00 gram sample of gold have if its density is known to be 19.3 g/cm3?

The volume of a substance when given the density and mass can be found by using the formula

[tex]volume = \frac{mass}{density} \\[/tex]

From the question we

mass = 200 g

density = 19.3 g/cm³

[tex]volume = \frac{200}{19.3} \\ = 10.362694[/tex]

We have the final answer as

Hope this helps you

choose the correct description of viscosity. under what conditions does magma have high viscosity?

I don't see the answer choices but we know that high viscosity means thick substances like peanut butter, honey, and mollases.

Magma has high viscosity when it is cooling down and decreasing in temperature. I hope this helps. I don't really know how to explain it.

Magma is defined as the hot liquid and the semi-liquid rock which is located under earth's surface. The flow of magma onto the earth's surface is called the lava .

What is viscosity?

Almost all fluids have some resistance to movement and we call this resistance as the viscosity . This property of the fluid is mainly due to the relative motion among the layers of the fluid. The SI unit of viscosity is poiseiulle (PI).

The viscosity of liquids generally decreases rapidly with an increase in temperature . The viscosity does not change as the quantity of matter changes. Hence it is an intensive property .

The low temperature and high concentration of SiO₂ are the conditions at which magma have high viscosity . The magma at high temperature have only low viscosity and also at low concentration of SiO₂.

Thus the viscosity of magma mainly depends on the composition and temperature of magma.

To know more about viscosity , visit;


Details : choose the correct description of viscosity. under what conditions

1. Describe one model for the structure of the nucleus. 2. Describe what makes a nucleus stable or unstable. ​

The structure of a nucleus encompasses the nuclear membrane, nucleoplasm, chromosomes, and nucleolus. The nuclear membrane is a double-layered structure that encloses the contents of the nucleus. ... A fluid-filled space or perinuclear space is present between the two layers of a nuclear membrane.

An atom is stable if the forces among the particles that makeup the nucleus are balanced.

C.1 Convert 25 miles per hour into meters per second. Use the following conversion ratios. ----1 mile/1.609 km ---- 60 seconds / 1 minute ---- 60 minutes / 1 hour C.2 What is the equation to convert °C to K Convert 100 °C into Kelvin What is the equation to convert °F to °C Convert 100 °F to °C C.3. Show your work is worth more than answering this right. Use the sideways T method or the table method below to show your work. Convert 1 foot to kilometers. Use the following conversions ratios. 1 foot = 12 inches. 1 inch = 0.0254 meters. 1000 meters = 1 kilometer.

The conversion of 25 miles per hour into meters per second using the

given conversion ratios is  [tex]\mathbf{ \dfrac{1609\ meters}{144 \ seconds}}[/tex] .

Conversion ratios are used in metric systems for changing one unit to another using the standard conversion numbers.

Given that:

  • 1 mile = 1.609 km
  • 60 seconds = 1 minute
  • 60 minutes = 1 hour

To convert 25 miles/ hour to meter/seconds , we have:

[tex]\mathbf{=\dfrac{(25 \times 1.609) \ km}{(60 \times 60) \ seconds}}[/tex]

  • Since 1 km = 1000 meters.
  • It implies that;

[tex]\mathbf{=\dfrac{(25 \times 1.609 )\times 1000 \ meters}{(60 \times 60) \ seconds}}[/tex]

[tex]\mathbf{= \dfrac{40225 \ meters}{3600 \ seconds}}[/tex]

[tex]\mathbf{= \dfrac{1609\ meters}{144 \ seconds}}[/tex]

  • The equation to convert  °C to K is  °C = 0 + 273.15 K

The conversion of celsius to kelvin can be achieved by the addition of the given amount of celsius rate with the constant 273.15 K.

To convert   100 °C into K we have:

  • 100 °C = 100 + 273.15 K
  • = 373.15 K  

To convert °F to °C, we use the equation:

[tex]=\mathbf{(^0 F - 32)\times \dfrac{5}{9}}[/tex]

To convert 100 °F to °C , we have:

[tex]= \mathbf{(100^0 F - 32)\times \dfrac{5}{9}}[/tex]

[tex]= \mathbf{(68^0 F)\times \dfrac{5}{9}}[/tex]

To convert 1 foot to kilometers by using the standard conversion ratios , we have the following;

  • 1 foot = 12 inches.
  • 1 inch = 0.0254 meters.
  • 1000 meters = 1 kilometer.

[tex]=\mathbf{\Big(\dfrac{12 * 0.0254}{1000}} \ kilometer \Big )\[/tex]

= 0.0003048 kilometers

Therefore, we can conclude that 25 miles per hour into meters per

second is  [tex]\mathbf{ \dfrac{1609\ meters}{144 \ seconds}}[/tex].

Learn more about conversion ratio here:


Shown here is a person shaving. Under magnification, the shaving foam might look like the image above the shaver. What type of mixture does the foam demonstrate? Give your reasoning.A man scrapes shaving cream from his face with a razor; an inset shows a rough-textured substance.

Shaving Foam is a Gas-Solid solution, as the gas is the aerosols, and the solid is the cream chemicals themselves. hope this helps! M48.

The element Carbon has an atomic number of 6 and an atomic mass of 12. What are the number of subatomic particles found inside the nucleus?

An atomic mass of 12 means carbon, and its atomic number is 6.

Details : The element Carbonhas an atomic numberof 6 and an atomicmass of 12.

Octane has the following chemical equation. C8H18 B.1 How many atoms of Carbon C are in 3 molecules of Octane 3C8H18 B.2 How many atoms of Hydrogen H are in 2 molecules of Octane 2C8H18

2 multiples 18 giving 36atoms.

3 times 8 equals 24 atoms.

An equatorial biome with high tempertures and distinct wet and dry seasons is a

In the equatorial regions there is no dry season, so it has nothing to do with that.

An equatorial biome with high tempertures and distinct wet and dry seasons is a temperate grassland.

A biome is defined as a community of  plant and  animals which covers a huge geographical area. The boundary of biomes on land can be determined by climate . Therefore, a biome is considered  as the total abundance of plants and animals interacting within specific climate conditions

The Temperate grassland can be characterized by variations in seasonal temperature . They have  annual fluctuations in temperature during hot summers and very cold winters. In deserts, they have a vast difference in temperature between the summer and winter season, which may vary over 40°C.

To know more about biome here


what does synthetic resource mean?

please help me ill give brainlest​

[tex]hope \: it \: \: helps \: \: u \\ ray4918 \: \: here[/tex]

Details : please help me ill give brainlest

Select the correct answer. The diagram shows how wind can push warm surface water away from an area to be replaced with cold, nutrient-rich water from deep in the ocean. What is this process called? A. chemosynthesis B. drainage C. evaporation D. upwelling

To describe an object´s motion , you need to known both its speed and its_______​

Hope this helps.

I need help with the second question, can anybody help me?

There are 1440 minutes in a day. Which means that there is 266400 minutes in 185 days. And in scientific notation it is: 2.66 · 10⁵.

During gas exchange, oxygen moves into the blood and carbon dioxide moves into the alveoli. True False

During gas exchange,oxygen moves into blood and carbon dioxide moves into the alveoli.

Hope its help

Details : During gas exchange, oxygen moves into the blood and carbon dioxide

Object: Dimensions = 5.0 cm 8.0 cm 6.5 cm Mass = 650 g Density =


All I need are the answers for 11, 12, 13, 2, 5,6

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  • ‘don’t underestimate how far you can go, as a uno graduate,” distinguished


Distinguished alumni, ‘don’t underestimate how far you can go, as a uno graduate,” distinguished alumna sabrina farmer tells gala audience.

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UNO alumna Sabrina Farmer (left) stands with President Kathy Johnson and  Ricky Burke, president of the UNO Alumni Association, at the Distinguished Alumni Gala held Thursday, Nov. 9, 2023 at the National WWII Museum.

UNO alumna Sabrina Farmer (left) stands with President Kathy Johnson and Ricky Burke, president of the UNO Alumni Association, at the Distinguished Alumni Gala held Thursday, Nov. 9, 2023 at the National WWII Museum.

Addressing a crowd of 400 people might be a daunting task to some. But Sabrina Farmer, who spoke to such a group inside the Boeing Freedom Pavilion at the National WWII Museum, is used to performing under pressure. As vice president of engineering at Google, Farmer is one of the company’s few employees who has worked on every single one of Google’s products, which means she makes decisions that impact billions of people and make billions of dollars.

She was honored Thursday as the winner of the 2023 University of New Orleans Homer L. Hitt Distinguished Alumni Award at the Distinguished Alumni Gala presented by Energy and Google. Avril Habetz, managing partner for Northwestern Mutual of Louisiana and Mississippi, was named the 2023 Norma Jane Sabiston Distinguished Young Alumna of the Year. The four academic colleges and Privateer Athletics also honored distinguished alumni.

Farmer is the 40th honoree to receive the Homer L. Hitt Distinguished Alumni Award. A native of Marrero, La., she earned a bachelor’s degree in computer science from the University. A year after graduating, she founded the Scholarship for Women in Computer Science at UNO.

“I credit UNO for everything I’ve accomplished,” said Farmer, who participated in a fireside chat-style conversation with Habetz and emcee Clancy DuBos. “I felt like UNO made a bet on me, and I felt like I needed to pay them back the entire time.”

Farmer, who said she was the first woman in her extended family to attend college, helped rewire computer labs in the computer science department as a student. It sparked an interest in problem-solving that has continued to drive her throughout her career. She said UNO provided a foundation for her professional growth that is unsurpassed.

“What I tell students now is don’t underestimate how far you can go as a UNO graduate. I have worked with people from Cal Tech, MIT, Harvard and Princeton, and let me tell you, I can totally hold my own,” Farmer said.

Habetz oversees the market development of eight district offices in two states. She began her career at Northwestern Mutual in 2007 as an executive assistant. Since then, she’s taken on greater responsibilities in various leadership roles, and, in June of 2023, she was promoted to managing partner of Louisiana and Mississippi. She encouraged recent UNO graduates to seek out both mentors and sponsors.

“The difference between a mentor and a sponsor is a sponsor is going to be an advocate for you when you’re not there,” Habetz said. “They’re going to be the person in the room when you’re not in the room to help you further the development of your career.”

•    The College of Business Administration honored Joseph M. Dempsey, chief financial officer of Crescent Crown Distributing, LLC. •    The Dr. Robert A. Savoie College of Engineering honored Kimberly S. Cook-Nelson, executive vice president of nuclear operations and chief nuclear officer of Entergy. •    The College of Liberal Arts, Education and Human Development honored Jericho Brown, a Pulitzer Prize-winning poet and director of creative writing at Emory University. •    The College of Sciences honored Frank Juge Jr., an emeritus professor of chemistry at the University of Central Florida. •    Privateer Athletics posthumously honored Wayne Cooper, who played for 14 years in the NBA and served as an NBA executive for another two decades. His award was accepted by his widow, Denise.

The Distinguished Alumni Gala was also the first major alumni event attended by the University’s new president, Kathy Johnson, who assumed her role earlier this month.

“The collective contributions of alumni are the legacy of the University of New Orleans,” Johnson said. “I take such pride in learning about those being honored tonight and those that have been honored in the past. Each of you helps to influence the culture and the reputation of UNO through your actions, your advocacy and your relationships with others.”

In addition to the fireside chat, attendees were treated to a selection of poems read by Brown, who earned his MFA from UNO and has published three collections of poetry.

how to solve an engineering problem

Scholarship Honoring Longtime History Professor Günter Bischof Will Support Student Research and Travel

Tony Diaz’s book on community organizing, published by UNO Press, recently earned international recognition.

UNO Press Book Wins International Latino Book Award

University of New Orleans biology professor Nicola Anthony, far left in blue, conducted research in Gabon, Africa as part of a field training school. This photo was taken in front of the mayor’s office in Lastourville.

UNO Biology Professor Nicola Anthony Helps Train Conservation Scientists Via Field School in Central Africa


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