Calculating Work for Pumping Liquid in a Vertical Cylindrical Tank

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    Liquid Work
In summary, to pump the liquid from the bottom to the top of a vertical right circular cylindrical tank measuring 32 feet high and 8 feet in diameter, with a liquid weight of 62.4 lb / ft^3, the correct calculation would involve finding the volume of the cylinder (pi*r^2*h), multiplying it by the weight of the liquid, and then finding the work required by integrating the resulting function from 0 to 32. The actual correct answer is 1,605,922 ft-lb.
  • #1
whatlifeforme
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Homework Statement


A vertical right circular cylindrical tank measures 32 feet high and 8 feet in diameter. It is full of liquid weighing 62.4 lb / ft^3 How much work does it take to pump the liquid to the level of the top of the tank?


Homework Equations


h=32
d=8 (radius = 4)
liquid weight = 62.4 lb / ft^3


The Attempt at a Solution


1. integral (0 to 32) (62.4x) dx
2. (156/5)x^2 | (0 to 32)
3. answer: 31,948.8

actual correct answer: 1,605,922 ft-lb
 
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  • #2
whatlifeforme said:

Homework Statement


A vertical right circular cylindrical tank measures 32 feet high and 8 feet in diameter. It is full of liquid weighing 62.4 lb / ft^3 How much work does it take to pump the liquid to the level of the top of the tank?


Homework Equations


h=32
d=8 (radius = 4)
liquid weight = 62.4 lb / ft^3


The Attempt at a Solution


1. integral (0 to 32) (62.4x) dx
This (above) is way off.

Have you drawn a sketch of a typical "layer" of water? Each of the layers has the same volume, and hence the same weight, but a layer at the bottom of the tank has to be lifted all the way to the top, while the layer at the top doesn't have to be lifted at all.

I don't see any accounting for this in your work.
whatlifeforme said:
2. (156/5)x^2 | (0 to 32)
3. answer: 31,948.8

actual correct answer: 1,605,922 ft-lb
 
  • #3
hi whatlifeforme! :smile:

ok-ish, but you haven't used the area of the cylinder! :wink:
 

1. What is pumping liquid?

Pumping liquid is the process of moving a fluid from one location to another using a pump. This can be done for various purposes such as transportation, mixing, or processing.

2. How does pumping liquid work?

Pumping liquid works by using a pump to create pressure and move the liquid through a series of pipes or channels. The pump typically has an inlet and outlet, where the liquid enters and exits respectively. By creating pressure, the pump is able to push the liquid through the system.

3. What factors affect the efficiency of pumping liquid?

The efficiency of pumping liquid can be affected by various factors such as the type and size of pump used, the viscosity of the liquid, the distance the liquid needs to be pumped, and the presence of any obstacles or obstructions in the system.

4. How is the flow rate of pumping liquid determined?

The flow rate of pumping liquid is determined by the pump's capacity, which is typically measured in gallons per minute (GPM) or liters per second (L/s). The flow rate can also be affected by the size and speed of the pump, as well as the size and type of pipes used in the system.

5. What are some common applications of pumping liquid in scientific research?

Pumping liquid is commonly used in scientific research for tasks such as circulating and mixing chemicals, transferring biological samples, or creating a controlled flow of liquid for experiments. It is also used in industrial and manufacturing processes for tasks such as cooling, cleaning, and transporting liquids.

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