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Find the total amount of work required to pump a liquid through the pipe at the top with a weight density of p=10N/ m^3 if the tank below is filled to a depth of 2m.

Find the total amount of work required to pump a liquid through the pipe at the top with a weight density of p10N m3 if the tank below is filled to a depth of 2 class=

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Solution

For this case we can do the following

V_L= L*w*h = 8*w*delta x

then we can create the following relation:

3/3 = (3-x)/w

w = 3-x

Then replacing in the slice volume we have:

V_L = 8*(3-x)*delta x

The force is given by:

F= rho * V_L = 10 N/m^3 * 8* (3-x)* delta x

Displacement = 2+x

then the total work is given by:

[tex]\int ^3_010\cdot8\cdot(3-x)\cdot(2+x)dx=1080[/tex]

If we solve the integral we got:

1080 J

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