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October 25th, 2011, 09:04 PM   #1
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Work to pump out a tank

The hemispherical tank shown is full of water. Given that water weighs , find the work required to pump the water out of the tank.



My Attempt:

The volume of a sample cross section is

The mass of the cross section is

The force need to lift this section is

The work needed to lift this section is


The do not give limits so I am assuming [a b]

Integrating we have






finally giving



I don't know if this is correct?
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October 26th, 2011, 11:49 AM   #2
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Re: Work to pump out a tank

For a circle of radius 5 with center (0,5), we have





The force increment can be written as:



The disc y feet from the bottom must be moved a distance of 5-y feet.

So, we have



Another way to set it up:



Both give the same result.
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October 27th, 2011, 06:15 AM   #3
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Re: Work to pump out a tank

Hey, Thx for the reply/help.

Why did you set the center at (0,5)?
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