Farmers often depend on elevated water storage tanks to supply water

Question

Farmers often depend on elevated water storage tanks to supply water for irrigation using gravity and pipes. The tanks are filled using a pump that draws water up from a source through a pipe. The pumps used are rated for their ability to move water through systems of pipes of certain sizes and designs. In the United States, this rating is expressed in either pounds per square inch (psi) or vertical feet. (Note that, in a vertical column of water, the pressure at the bottom is about 0.43 psi per vertical foot in the column.) That is, a pump rated for x feet can operate a pumping system of up to x total vertical feet. For example, the total vertical feet of a pumping system of the type above is the sum of

- the vertical distance of the pipe between the surface of the water source and the pump;

- the vertical distance of the pipe between the pump and the top of the elevated tank; and

- the resistance from friction when water moves through the pipes, which is increased by angled pipes and smaller diameter pipes, expressed in vertical feet as a measure of the pump’s resultant loss in capability.

chetan2u · Accepted Answer

Q.1 Assume that with the farmer’s plan the resistance from friction in the system will contribute exactly 5 vertical feet to the system’s total. For each of the following possible heights from the surface of the water source to the top of the tank, select Yes if it meets the constraints of the plan as specified. Otherwise, select No.

The constraints are the pressure in psi, which depends on vertical height and vertical height itself.
Vertical height: The vertical height is 58 feet, and it contains 5 feet of vertical height lost due to the resistance. Thus effective 53 feet.
Clearly anything above 53 feet cannot be met out of existing pump.

20 feet:  <53 feet, so can be used. Let us check the pressure now. The inlet is 4 above ground and 5 feet above the water surface. Thus, pressure is 0.43psi*(20-5) = 7.95, which is less than the pressure required 10 psi.
Hence will not work...NO

40 feet:  <53 feet, so can be used. Let us check the pressure now. The inlet is 4 above ground and 5 feet above the water surface. Thus, pressure is 0.43psi*(40-5) = 15.05, which is more than the pressure required 10 psi.
Will work...YES

60 feet:  >53 feet, so can not be used...NO

Q.2. The farmer is considering replacing the water pump that is in place with one that has the same rating but cannot pump as many gallons per minute. For each of the following statements, select Yes if, according to the information provided, it describes a likely result of this change. Otherwise, select No.
 
(a) The maximum diameter of the pipe the farmer could feasibly use between the pump and the water tank would be smaller.
(b) The maximum distance between the water tank and the ground would be smaller.
(c) The maximum distance between the irrigation system inlet and the ground would be smaller.
 We can safely mark NO for all as there is no link given between Pumping speed in Gallon per minute and any attribute of the pump or layout.

Q.3. Assume the farmer’s irrigation system has been completed as described. If all other specifications remain unchanged, which one of the following changes would, if made, result in an increase in the pounds per square inch (psi) at the bottom of the pipe between the water tank and the irrigation system? 
 The psi depends on the vertical height and increase with increase in vertical height above inlet. 
Let us see which option increases the vertical height above the inlet.
(a) Increasing the height of the pump inlet.... Reduces the distance between top of tank and the inlet of pump as top is fixed, resulting in decrease in vertical height above inlet 
(b) Decreasing the height of the water tank.... Reduces the distance between top of tank and the inlet of pump as pump inlet is fixed, resulting in decrease in vertical height above inlet 
(c) Increasing the number of gallons per minute the pump pumps... No relation 
(d) Decreasing the height of the irrigation system inlet.... This increases the distance between top of tank and the inlet of pump as top is fixed, resulting in increase in vertical height above inlet ..ANSWER
(e) Decreasing the capacity of the water tank... No change if the height remains the same. But will reduce if the same capacity is in a larger tank

demawtf · Answer

Why on earth is "Difficulty: 555-605 Level"?

Noida · Answer

Why are we using 5 feet to calculate pressure? Shouldn't 4 feet be substracted to find the pressure?

The question says that a vertical column of water exerts 0.43 psi. Why are we taking water level and not ground level to calculate psi?

chetan2u

chetan2u · Answer

The wordings in the questions are 
 For each of the  following possible heights  from the surface of the water source  to the top of the tank , select Yes if it meets the constraints of the plan as specified. Otherwise, select No.

So, 20' is above surface of water source.

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined automatically based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question. For reading comprehension questions, the difficulty level is the average of the difficulties of the individual questions.

Gemmie · Answer

1. Assume that with the farmer’s plan the resistance from friction in the system will contribute exactly 5 vertical feet to the system’s total. For each of the following possible heights from the surface of the water source to the top of the tank, select Yes if it meets the constraints of the plan as specified. Otherwise, select No.

psi of the pump: 58
friction: 5
==> actual psi of the pump: 58 - 5 = 53 (verticle feet)

20 feet => No

+) 20 < 53 => do not exceed the max psi of the pump(i.e 53 verticle feet)

+) psi at the inlet: 0.43 * (20 - 1 - 4) = 0.43 * 15 = 6.45 < 10 (required min psi)

40 feet => Yes

+) 40 < 53 => do not exceed the max psi of the pump(i.e 53 verticle feet)

+) psi at the inlet: 0.43 * (40 - 1 - 4) = 0.43 * 15 = 15.05 > 10 (required min psi)

60 feet => No

53 < 60 => exceed the max psi of the pump(i.e 53 verticle feet)

2. The farmer is considering replacing the water pump that is in place with one that has the same rating but cannot pump as many gallons per minute. For each of the following statements, select Yes if, according to the information provided, it describes a likely result of this change. Otherwise, select No.

Answer for all 3 are No because the sources do not mention anything about the pumping speed (gallon/minute).

3. Assume the farmer’s irrigation system has been completed as described. If all other specifications remain unchanged, which one of the following changes would, if made, result in an increase in the pounds per square inch (psi) at the bottom of the pipe between the water tank and the irrigation system?

D. Decreasing the height of the irrigation system inlet

Tab 1: In a vertical column of water, the pressure at the bottom is about 0.43 psi per vertical foot in the column

==> To increase the psi at the bottom btw water tank and the irrigation system, we need to ỉncrease the length of the pipe btw these 2

==> Either inrease the height of the tank orr decrease the height of the irrigation system

darthvader20 · Answer

Hello, could you please elaborate this solution? how did we get "58" as the max?

UDEMYtutorJackson · Answer

As per the Farmer's plan the pump has a rating of 58 vertical feet.

So there are 2 things to consider when we decide the tank height 
1.Will the water that flows from the tank to the irrigation system have the necessary psi 
2.Is the pump able to get the water to the tank

1.Will the water that flows from the tank to the irrigation system have the necessary psi :  
20 feet - it's a NO because the water flowing from the tank will not have sufficient psi 
Why so ? 
It's given that per vertical foot the pressure at the bottom is about 0.43 psi
The irrigation system is 4 feet above ground as per diagram. So, 20-4 = 16 feet
so for 16 feet = 16*0.43 which is less than 10 psi (as per Farmer's plan, the irrigation system, requires at least 10 pounds per square inch (psi) of pressure at its inlet to operate;)

2.Is the pump able to get the water to the tank  
A.40 feet - will give > 10 psi at the outlet hence not a concern. (40 -4 = 36. 36 * 0.43 is greater than 10) 
B.The pump can get water up a total of 40 feet + 5 feet (accounts for friction) = 45 feet. 
45 < 58 , so it's a YES

3.60 feet > 58 feet  , clearly No

HarshavardhanR · Answer

Question 1:
(1) The farmer bought a pump rated 58 feet. But actual ability i.e., to what height it can actually pump will also depend on the friction resistance of the system in which the pump will be fitted. This is given -> 5 feet. So, the pump can pump to a max of 58 - 5 = 53 feet when it is part of this system. Keep this in mind.

(2) Pressure at the inlet of the irrigation system must be at least 10 psi.

How to calculate this pressure? 0.43 x (vertical height of water till the inlet point) = 0.43 * (8+x) (refer diagram). This must be >=10 psi.

The question asks -> If, for the given heights from water surface to tank top (5 + 8 + x), the constraints of the plan are met, then choose Yes. Else, No.

___
Harsha

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HarshavardhanR · Answer

Q3:  https://gmatclub.com/forum/download/file.php?id=82639 
1) Increasing the height of the pump inlet -> Does not reduce 8+x (distance between tank top and IS inlet). So, this will not impact the psi.
2) Decreasing the height of the water tank -> This will actually reduce 8 + x rather than increase it. This will reduce the psi.
3) Increasing number of gallons/min the pump pumps -> This has no impact on the height 8+x, which is what matters for psi.
4)  Decreasing the height of the IS inlet. This will increase x, thus, increasing 0.43 (8+x). Correct. 
5) Decreasing the capacity of the water tank -> Again, because this has no tangible impact on the height 8+x, this should not have the desired impact.

Choice D.
___
Harsha

KarishmaB · Answer

Since this question has been causing a lot of trouble, here is its video solution:

https://www.youtube.com/watch?v=pQmUy_r4SbM

rish_dutton · Answer

Q3 OFFICIAL EXPLANATION

Assume the farmer’s irrigation system has been completed as described. If all other specifications remain unchanged, which one of the following changes would, if made, result in an increase in the pounds per square inch (psi) at the bottom of the pipe between the water tank and the irrigation system?

Infer 
This question asks which change would result in an increase in the pounds per square inch (psi) at the bottom of the pipe between the water tank and the irrigation system—that is, at the irrigation system inlet—assuming all other specifications remain unchanged. We are told in the Pumping Systems information that the pressure at the bottom of a vertical column of water is about 0.43 psi per vertical foot in the column. Therefore, any change that would increase the height of the column of water above the irrigation system inlet would increase the pressure at that inlet. Suppose that the height of the irrigation system inlet was decreased, but nothing else was changed, such as the height to the top of the water tank. The result would be that the height of the water column above the inlet would increase. Therefore, given that the psi at the irrigation system inlet (that is, at the bottom of the pipe between the water tank and the irrigation system) is about 0.43 psi per vertical foot in the column, decreasing the height of the irrigation system inlet would result in an increase in the psi at the bottom of the pipe between the water tank and the irrigation system.

The correct answer is Decreasing the height of the irrigation system inlet.

CORRECT: D

Hoehenheim · Answer

Hi  chetan2u  
Great solution. Shouldn't the effective height in Q1 also consider the height of tank? Although it doesn't affect the answers, I think it should be like:
20 feet:- 20(water to tank top) - 5(system height above water) - 8(height of tank). This gives us the length of pipe (column - tank height).
Similarly for 40feet, pressure= 11.63psi

Reason to do this is because the minimum pressure at the inlet should be 10 psi or more. The minimum pressure of the column will be when the water level in the tank is at very bottom. Otherwise the system will stop functioning when the water level in tank reaches any level less than what corresponds to 10psi pressure at the inlet.

Am I correct to understand it this way? Also I guess to avoid this debate, GMAC did not put in values between 20 and 40.

Dbrunik · Answer

this is just bananas lol

Sungbin · Answer

this is in the official guide?damn tooo hard

kayarat600 · Answer

The biggest lie here is itching marked as non math related

StanleyVu · Answer

Dear Sir,
Where from the question can we deduce the equation of the pressure as 0.43psi*distance from the water surface?

MegB07 · Answer

Hi Karishma, the video was helpful. I just didnt understand how did you come to the 10/0.43 ft height?

jenneyennej · Answer

why b school needs to know these physics?

Farmers often depend on elevated water storage tanks to supply water

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Yes	No
		The maximum diameter of the pipe the farmer could feasibly use between the pump and the water tank would be smaller.
		The maximum distance between the water tank and the ground would be smaller.
		The maximum distance between the irrigation system inlet and the ground would be smaller.

	Increasing the height of the pump inlet
	Decreasing the height of the water tank
	Increasing the number of gallons per minute the pump pumps
	Decreasing the height of the irrigation system inlet
	Decreasing the capacity of the water tank

GMAT Multi-Source Reasoning (MSR) Questions

Farmers often depend on elevated water storage tanks to supply water

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