Calculating Pump Power for Well Water Removal

[Akash47]

Homework Statement

A well has a diameter of 6 m and a height of 15 m.2/3 of volume of the well is filled with water.A pump can vacate 1/3 of volume of water from the well in 7 minutes 20 seconds.What is the power of the pump?

Homework Equations

W=mgh, P=W/t

The Attempt at a Solution

The question can be solved easily by using the given equations.But I don't know how I will find the mean displacement of center of gravity.Actually I don't have any idea about this (the part in bold line).So I want a clear concept about it.

 

[phyzguy]

Why don't you try making a sketch of where the water is before and after the pumping process?

 

[Akash47]

Why don't you try making a sketch of where the water is before and after the pumping process?

I am sure that you haven't understand my problem clearly .I have already made a sketch of the problem but I haven't any idea about mean displacement of center of gravity.I just want a clear concept about this and nothing else.

 

[berkeman]

I am sure that you haven't understand my problem clearly .I have already made a sketch of the problem but I haven't any idea about mean displacement of center of gravity.I just want a clear concept about this and nothing else.

Have you tried thinking about it using a simple integration, and then comparing that to the answer you get by using the center of the water column for the mean displacement? Or even simpler, you don't have to set up the integration, just consider different cases with different "pieces" of the water being taken out separately. Start with one whole piece with the center of mass in the center of the water column, and lift that center up to ground level. Then cut the column in half, and do the same for the two separate water columns and their centers of gravity. Then do the case cutting the water column into 4 pieces, and so on...

 

[haruspex]

I haven't any idea about mean displacement of center of gravity.I just want a clear concept about this and nothing else.

it means figuring out where the mass centre of the pumped water is before and after pumping and taking the vertical difference between the two.

 

[Akash47]

it means figuring out where the mass centre of the pumped water is before and after pumping and taking the vertical difference between the two.

Thanks.