Question

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.

Answer 1

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:

`\int ^3_010\cdot8\cdot(3-x)\cdot(2+x)dx=1080`

If we solve the integral we got:

1080 J