A Technique for Solving Engineering Word Problems
You may think that solving a problem expressed in a word format is just another
way of giving a test question, but these types of problems are an attempt to pose a
question in a real world situation. It is an attempt to give you practice in working
through a series of questions and arrive at a solution. It’s a surrogate for how you
will receive a task in your work environment. Your supervisor will relay a task to
you verbally in a series of questions and statements and you will need to take notes,
ask questions and pose the problem to yourself in the form of a word problem. You
will then have to develop the equations to solve the problem. The important skill
you need to develop is reading for content which is much more intense than reading
for pleasure.
How to read for content – a multistep approach: Reading for content requires
reading the problem three to four times at a minimum. This is how I do it:
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First read the problem to obtain a familiarization to the question and
the information given to solve the problem.
Next, read the problem to determine the question or questions being
asked. Underline each question and write the question(s) out in your
notebook.
Next, read the question again to determine the givens. Write down
the givens with their units in your notebook under the questions. Be
sure you don’t skip writing down the units. They can be key to
checking your solution. If you get the units correct, you probably
solved the problem correctly. Also you may need to change the
units for proper use in the equation stated in the problem.
Read the problem statement again to determine if you missed
anything and to determine if there is extraneous information, which is
not needed to solve the problem.
Now you are ready to formulate the problem solution. Let’s solve some example
problems to get a feel for solving problems.
The first problem we will discuss is the
Garbage Truck Problem:
There are about 179,000 garbage trucks in the U.S. alone. Projecting that out to the
rest of the world based on the world’s population, there are 3.58 million garbage
trucks. A typical garbage truck travels 30,000 miles per year at 4 mpg. If all the
garbage trucks were converted to hybrid vehicles that get 25 mpg, how many
gallons of diesel fuel can be saved per year? How many lbs. of CO2 would be saved
per year? How many lbs. of Carbon would be saved?
Fact Sheet:
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CO2 Emissions from a gallon of diesel fuel = 22.4 Lbs. / gallon
Carbon emissions are 12/44ths of the CO2 emissions
Energy in a gallon of diesel fuel is 40 kWh/gal
There are 42 gallons in a barrel
Step 1: Read through the problem statement to get a general sense of the problem.
After doing this we surmise the problem states that a typical garbage truck gets very
poor gas mileage (4 mpg) and there are 3.58 million garbage trucks and they are
driven 30,000 miles per truck per year. We will need to answer questions on how
much fuel is saved if we convert the vehicle to a hybrid and on the amount of carbon
and CO2 saved.
Step 2: Let’s get more specific and write out the questions that need to be answered.
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Question 1: If all the garbage trucks were converted to a hybrid powertrain
that gets 25 mpg versus a standard powertrain that gets 4 mpg, how many
gallons of diesel fuel would be saved?
Question 2: How many lbs. of CO2 would be save by converting to hybrids?
Question 3: How many lbs. of Carbon would be saved?
Step 3: Read to determine the givens:
 There are 3.58 million Garbage trucks.
 Each truck travels 30,000 miles per year
 Hybrid trucks get 25 mpg
 Conventional trucks get 4 mpg
 CO2 Emissions from a gallon of diesel fuel = 22.4 Lbs. / gallon
 Carbon emissions are 12/44ths of the CO2 emissions
Step 4: Calculate total miles driven by the garbage trucks
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Total miles = 3.58 x 10^6 x 3.0 x 10^4 = 1.074 x 10^11 miles
Step 5: Calculate fuel used by conventional truck.
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Gallons used by conventional truck = 1.074 x 10^11 /4 mpg = 2.69 x 10^10
gallons.
Step 6: Calculate fuel used by hybrid truck.
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Gallons used by hybrid truck = 1.074 x 10^11/25 = 4.30 x 10^9 gallons
Step 7: Calculate gallons saved
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Gallons saved = 2.69 x10 ^10 – 4.30 x 10^9 = 2.26 x 10^10 gallons
Step 8: We can now calculate lbs. of CO2 and Carbon saved.
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Lbs. of CO2 saved = 22.4 lbs/gal x 2.26 x 10^10 = 5.05 x 10^11 lbs.
Lbs. of Carbon = 12/44 * Lbs. CO2 = 12/44*5.05 x 10^11 = 1.38x10^11 lbs or
6.26 tonne
We have now answered all the questions!
Let’s try a different type of problem. This one will be on solar energy.
Solar Energy Problem:
The Southwest region of the United States has a high level of solar energy striking
the earth. This is due to the number of sunny days per year and the latitude of this
region. The total area of the States that make up the southwest is 1 million square
miles. The amount of solar energy hitting this area is 8 kWh/m^2/day. If 2% of the
area is utilized for a commercial utility sized PV system, how many kWh per day
could be generated if the capacity factor of the facility is 0.2 and the latest NREL data
claim of an area density of 50 acres/MW is used? What percentage of the total US
electricity per day is this if the US uses 11 TWh/day.
Note: Recall that capacity factor (CF) = (# of hours actual / # hours available).
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CF = 0.2 = 4.8/24
1 Acre = 0.00156 Sq. Mile
1 Sq. mile = 2.59 x 10^6 meters squared
1 TWh = 1x10^12 Watt hours or 1x10^9 kWh
Solving the problem:
Step 1: Read through the problem for content. After the first read we surmise that
the question involves calculating the amount of solar energy that can be generated
by the hitting 2% of the area of the southwest region of the U.S. Also there are a lot
of data on energy density and a term called a capacity factor.
Step 2: Read the problem and find the specific questions being asked. After we read
for determining the specific questions, we can write out the questions as:
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If we install a Solar Photo Voltaic power system on 2% of the area of the
southwest states, how many kWh/day of energy can this system create?
What percentage of the total electricity used in the U.S. can this system
provide if the U.S. uses 11TWh/day?
Step 3: Read the problem again to determine the facts or data given that can be used
to solve the problem. Write down these facts.
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Use 2% of the area for the power-plant Area = .02 x 1 x 10^6 sq. miles
Intensity of the sun = 8kW/hr/m^2/day
Energy density of a solar PV system 50 acres/MW
Capacity factor = 0.2
Step 4: Read over and look at the units. Note we have energy given in kWh and TWh
and power expressed in MW. We will need to change units to a common base at
some point in the calculations. Also, we have areas expressed in acres and Sq. miles.
These need to be changed to the same base. We will need to make some
intermediate calculations to rectify the units.
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Since the area available is given in sq. miles, we will change the power
density to sq. miles/MW from acres/MW. This has the form:
o Sq. miles/MW = acres/MW x sq. miles/Acre. Putting in actual
numbers we get: Sq. miles/MW = 50 acres/MW x 0.00156 sq.
miles/acre or 0.078 Sq.miles/MW
Step 5: Calculate the available power;
o To calculate the power available we get:
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2 x 10^4 sq. miles/0.078 sq. miles/MW = 2.56 x 10^5 MW
But we also have a capacity factor of 0.2 so the actual power is
P = 0.2* 2.56 x 10^5 = 5.13 x 10^4 MW. Note the capacity
factor accounts for lack of sun etc.
Step 6: Calculate the energy produced per day.
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E/day = 5.13 x 10^4 MW x 24 hr/day = 1.23 x 10^6 MWh/day= 1.23
TWh/day or 1.23 x 10^9 kWh/day.
Step 6: Calculate % of total energy used per day.
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% Total = 1.23 TWH/day / 11 TWh/day x 100 = 11.2%
Let’s now look at a physics problem.
Problem Statement:
A meteor falls from the sky to the Earth. The meteor already had an initial velocity
downward when it was spotted. If it hit the Earth at 335 m/s after being seen for 30
seconds, then what was the initial velocity of the meteor?
Kinematic equations for physics problems:
Step 1: Read the question to get a general idea of what is being asked.
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This is a question asking the final velocity of a meteor that would hit the
earth.
Step 2: What is the specific question?
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What is the initial velocity of the meteor when you first spot it?
Step 3: What are the givens?
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Time t from initial spotting to impact is 30 sec.
Final velocity when the meteor hits earth is V final = 335 m/s
g = -9.8 m/s2
Step 4: Look at the givens and the equations to determine which equation to use.
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Givens are t and V final
The first equation has only these variables and is the correct one to use.
Write down the equation and then put in the numbers to solve
Vf = Vi – gt
335 = Vi + 9.8 x 30 or
Vi =335- 294 = 41 m/s