Work done by pumping water into a tank

In summary, the problem involves finding the work done in pumping water from a cylindrical tank with a circular base and varying height, given a water density of 9800 N/m^3. The volume of the tank is calculated using the formula ∏r^2*Δy and the weight of the water is calculated using 9800*4∏Δy. The distance the water needs to be pumped up is determined by the height of the tank at the bottom and the highest level. The final integral equation is ∫9800*4∏Δy*(10-y), from 0 to 4, which results in an answer of 1,254,400∏ N-m.
  • #1
jdroidxw
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0

Homework Statement



Problem with picture attached
I need help on 24. **24 is a continuation of 23 so use the same dimension except for the distance...

Or you can go here http://college.cengage.com/mathemat...alc8e_solution_main.html?CH=00&SECT=a&TYPE=se

Chapter 7, Lesson 5

Homework Equations



Volume=∏r^2*Δy
Water= 9800 N/m^3

∫(Volume)(water)(distance)=Work done ??

The Attempt at a Solution



Volume= 4∏Δy
Weight=9800*4∏Δy
Distance is where I'm not too sure about. Would I use (10-y)??
If so then I got...
∫9800*4∏Δy*(10-y), from 0 to 4 = 1,254,400∏ N-m

My answer looks really huge... Did I mess up anywhere?
 

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  • #2
Welcome to PF, jdroidxw! :smile:

You have the infinitesimal weight correct with 9800*4∏dy.

How far does the water that ends at the bottom have to be pumped up?
And how far does the water that ends at the highest level have to be pumped up?
 

1. What is the purpose of pumping water into a tank?

The purpose of pumping water into a tank is to store it for later use. This can be for various purposes such as household use, irrigation, or industrial processes.

2. How is the work done by pumping water into a tank calculated?

The work done by pumping water into a tank is calculated by multiplying the force exerted by the pump with the distance the water is lifted. This is known as the work-energy principle.

3. Does the height of the tank affect the work done by pumping water into it?

Yes, the height of the tank does affect the work done. The higher the tank, the greater the distance the water needs to be lifted, resulting in more work being done by the pump.

4. What factors can affect the efficiency of pumping water into a tank?

The efficiency of pumping water into a tank can be affected by factors such as the type and condition of the pump, the distance and height the water needs to be pumped, and the viscosity and temperature of the water.

5. How does the work done by pumping water into a tank impact the cost of water usage?

The work done by pumping water into a tank can impact the cost of water usage as it requires energy to operate the pump. The more work that needs to be done, the higher the energy consumption and therefore, the higher the cost of water usage.

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