Sarah J.

asked • 02/19/15

3 questions, and I have to use dimensional analysis for all of them with all work shown

You must use dimensional analysis for these problems. The set-up is important. There should be only one long conversion for each of the 3 problems below. Use only conversions are given or that you should know from book (common English system conversions).

1. The fuel consumption of a certain car is 24 miles per gallon. How many kilometers per liter is this? (1 mile is approximately 1.61 kilometers and 1 liter is approximately 1.06 quarts.) 

2. Experts estimate that when the levees around New Orleans broke in the aftermath of Hurricane
Katrina, water flowed into the city at a peak rate of 9 billion gallons per day. There are 7.5 gallons in one cubic
foot.

2a. Flow rate is the volume of water that entered the city during a given unit of time. Change the flow rate that
is given as 9 billion gallons per day to units of cubic feet per second (cfs).

2b. Assume that the flooded part of the city had an area of 6 square miles. Estimate how much (in feet) the
water level rose in one day at the given flow rate. Hint: Start with the original information; don’t use part a.
 
Please help! Thank you!
 

1 Expert Answer

By:

Norman M. answered • 02/19/15

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Sarah,
 
Each of the problems should be set up in a similar manner, start with the unit given, then use conversion factors to get to the unit desired.  The unit on top in one factor should be on the bottom of the next.  I will do the first for you, and if you have any other questions, comment and I will help with more.
 
(24mi/1g)(1.61km/1mi)(1g/4qt)(1.06qt/1L)=10.24km/L
 
I hope this helps.
 
Norm.
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Sarah J.

Thanks, I got the same answer for the first one. Although, I'm stuck on the second one. So far I did, (7.5gal/1cubic ft)(27 cubic ft/1cubic yd)(1 cubic yd/9square feet) and I'm stuck there for how to get it converted to 9 billion gallons/day
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02/19/15

Norman M.

So, you should start with the 9 billion gallons per day and convert it to cubic feet per second.  That is why you are stuck.  Start like this:
 
(9x10^9gal/day)(1ft^3/7.5gal)   Then convert the day into hours, then minutes, then seconds.
 
 
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02/19/15

Sarah J.

Oh okay. So how does the cubic feet unit cancel out? Is the answer 13888.89?
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02/19/15

Norman M.

You don't want the cubic feet to cancel.  The way it is setup now, it is giving you cubic feet per day.   Now continue the conversions to convert days to hours and then hours to minutes, and finally minutes to seconds. 
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02/19/15

Sarah J.

Yes, so I continued the conversions: (9x10^9gal/day)(1ft^3/7.5gal)(1day/24 hrs)(1hr/60min)(1min/60 sec) and I got 13888.89
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02/19/15

Norman M.

Yes, that is the correct answer.
 
Are you ok on the next one?
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02/19/15

Sarah J.

Would the units be cubic feet/second? And for the next one I got the same answer... Is that correct? 
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02/19/15

Norman M.

For 2a, yes, the units would be in cubic feet per second, which is what the question asked for when it said cfs.
 
2b is a bit more complicated.  Basically, you need to find the volume of water in cubic feet, and divide that by the square foot area it covered, and that will give you the depth of water in feet.
 
Here is how I did it...
 
((9x10^9 gallon/1day)(1ft^3/7.5gallon))/(6mile^2(5280ft^2/1mile^2))=7.17ft
|---------------------------------------------| |--------------------------------|
          Numerator                                           Denominator
 
I hope that is clear... 
 
 
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02/19/15

Sarah J.

I'm still a little confused... How would I put that into dimensional analysis form?? So would (9*10^9) gallon be on top and then over 1 day...? or Would that all be in the numerator..?
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02/19/15

Norman M.

Sorry, in this editor it is hard to input things the way you would do them.
 
The numerator would be (9x10^9gallon/1day)(1ft^3/7.5gallon)
 
The denominator would be (6mile^2(5280ft^2/1mile^2)
 
The answer is 7.17 ft.
 
(9x10^9gallon/1day)(1ft^3/7.5gallon) = 7.17ft
(6mile^2(5280ft^2/1mile^2)
 
I hope that is more clear.
 
 
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02/20/15

Sarah J.

How does the day cancel out? Also for the answer I keep getting 37878.78...
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02/21/15

Norman M.

The day won't cancel out, because the question is asking how many feet the water rose in one day and the original data listed the flow rate per day, so you don't want the day to cancel.
 
As for the answer....  tell me what you are entering into the calculator button by button, and I may be able to help.
 
 
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02/21/15

Norman M.

I found the mistake...  you are dividing by 5280, not by 5280^2. 
 
The unit on top is volume in ft^3, you are dividing by ft^2 to be left with feet in only one dimension.
 
Does that make sense?
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02/21/15

Sarah J.

Oh, okay. Now I understand it. And yes, I just got that same answer. Thank you so much!
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02/21/15

Norman M.

No problem.
I am waiting to get my profile approved on here for tutoring, but if you need any help, just let me know.
 
Norm.
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02/21/15

Sarah J.

Sounds good, thanks. 
 
So, just to double check, The answer for 1 is 10.24km
                                                                   L

The answer for 2a is 13888.89 ft^2
                                 seconds
 
The answer for 2b is 7.17 ft
                              day
 
Correct?
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02/21/15

Norman M.

Correct.
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02/21/15

Sarah J.

Hey, Norman. Would you be able to help me out with another problem please?
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03/07/15

Norman M.

Sure,
 
Whats up?
 
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03/07/15

Sarah J.

Here's the problem: 
 
The Shedd Aquarium's Caribbean Reef exhibit is a large, nearly cylindrical tank. The tank holds 90,000 gallons of water. The diameter of the tank is 12.2 meters. Even though the bottom of the tank is not flat, but is slightly deeper in the middle and shallower at the edges, pretend the bottom is flat and find the depth of the water in the tank in meters. Use 1 gal=3.785 L

The question asks to find the depth of the water in the tank in meters. 

Units should cancel to give final answer, in one long expression. We are to only use basic conversion units.
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03/07/15

Sarah J.

Nevermind, I got the answer. Thanks anyway!
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03/07/15

Taylor K.

Norman,
 
For problem 2a. you multiplied 9x10^9. how did you get the ten and the power of 9??
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03/07/16

Taylor K.

Never mind, I got it. dumb mistake
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03/07/16

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