Work Done by Pumping a Fluid

Now, how do we determine the amount of work needed to pump a fluid out of a container, especially if the container has an unusual shape?

Remember that in general:

In this case, the force is the weight of the fluid and the distance is the vertical distance the fluid must move upward. Remembering that the weight of the fluid is specific weight * volume:

Specific weight, g, is, of course, relatively constant, so we get:

We have already learned how to find an equation for dV, so we can substitute that into the equation above.

EXAMPLE