**
Problem
Solving in Engineering**

One of the primary tasks for engineers is often
solving problems.
It is what they are, or should be, good at.
Solving engineering problems requires more than
just learning new terms, ideas and concepts, and using rules and
laws.

To find out what engineering is really about, we
must learn how to apply these concepts and laws to real or
hypothetical situations. Experience has shown that this kind of
learning cannot occur without practice. This means spending more
time working problems than reading the text.

Problem solving is more than merely substituting
numbers in a mathematical formula. We should begin by studying
the ideas, the concepts, and their relationships first. Then we
should attempt the problems as a way to find out whether or not
we understand the subject.

**
Problem Solving Process**

In order to build a model and
solve the problem, the following steps may be followed:

1.
**Carefully
identify what is given in the problem.**
This is an important step because it makes things clear
before attacking the problem. Read the entire problem
carefully. You may need to briefly write down the question
using symbols, make lists or tables of known and unknown
information, and draw a diagram of the physical situation.

2.
**Carefully
identify the objective of the problem**.
This could be the most important step, because it becomes
the foundation for all the rest of the steps. What is the
problem asking you to solve or find? Sometimes the objective
of the problem is clear; some other times you need to lists
the unknown information in order to identify the objective.

3.
**Decide which
mathematical tool best suits the problem**.
What are the possible paths of solution to be followed? What
are the processes involved? What are the relationships
involved? And, determine which path and process promise the
greatest likelihood of success. This step will help you
build a collection of analytical methods, many of them will
work to solve the problem, and however, many others may not
work. Also, one method may produce fewer equations to be
solved than another, or it may require less mathematics than
other methods.

4.
**Write
equations and develop a model.**
After you decide on the method, document the process very
well by writing the equations to actually start solving the
problem.

5.
**Attempt a
solution.** Present detailed
solution before putting real numbers into equations.
Paper-and pencil, calculator, and computer tools are all
available to pursue the solution.

6.
**Verify the
solution.** Is it realistic,
expected, or not at all? Ask yourself whether the solution
you have obtained makes sense. Does the magnitude of the
answer seem realistic? You may want to rework the problem
via an alternative method to test the validity of your
original answer. By doing so, you develop your perception
about the most efficient methods to solve the problem. In
real life, any design is checked by several independent
means. Acquiring the habit of verifying the answer will help
you as a student and as an engineer in the future.

7.
Finally, if the
solution is realistic, present the solution to your
professor, boss, or team members. If not, then return to
step 3 and continue through the process again.

It is important to know that
although the above steps have been organized to apply to
engineering foundations types of problems, the problems to be
solved during one’s career will vary in complexity and
magnitude.

** **

As an example of the general
guidelines for problem solving, let us work a sample problem.

**Example**

Consider a tank that is
used to store a liquid. Liquid can be let into the tank through
an inlet pipe at the top, and it discharges from the tank
through an orifice
near the base. Such a situation occurs frequently in mechanical
and chemical engineering applications. Consider two cases for
the flow through the
orifice: laminar and turbulent.
What is the rate of outflow from the tank if the height of the
liquid is 0.5 m and the discharge coefficient is 0.7.

** **

**Solution**

** **

By reading the problem carefully
and drawing a diagram similar to the following Figure, we will
have covered steps 1 and 2.

A liquid storage system.

The basis of this
approach to model building is that the equations which
constitute a model are not arbitrary mathematical entities, but
have a consistent physical basis. There are certain types of
equation which describe different aspects of a model.

A knowledge of this
helps to ensure that all equations are written down. For step 3
recall the relationship between the volumetric rate of outflow
*Q* measured in (m^{3}/s) and the height of the
liquid *h* measured in (m).

** **

** **

where *C*_{d}
is a constant of proportionality called the discharge
coefficient. The discharge coefficient is
constant that depend on the shape of the orifice.

It could be a
sharp-edged, a short flush-mounted tube, or a rounded orifice.
In this example, we have assumed that the volumetric flow rate
of the liquid is proportional to the height only, however, in
practice the flow rate depends on the pressure drop across the
orifice, orifice cross-sectional
area, and fluid density.

The dependent
variable *Q* is a function of the independent variable *h*.
Therefore, the input function is the head h, the function rule
is “multiply the input by *C*_{d}”, and the
resulting output is the flow rate *Q*. A graph of *Q*
against *h* is shown in the following Figure.

A graph of *Q* and *h*
relationship for a laminar flow.

** **

If the flow through the
orifice
is turbulent then a different functional relationship will exist
between *Q* and *
h*

A graph of *Q* against *h*

A graph of *Q* against
*h*

Now in accord with step 5, we
substitute the values and the units for the algebraic symbols.
For laminar flow

** **

For turbulent flow

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