Question

A trapezoidal trough 6 meters long, 4 meters wide on top, 3 meters wide at the bottom and 2 meters deep is filled with water. Find the work needed to pump all the water out of the tank as well as the force against the wall of the container. Use kg/m³ as the density of water?

Answer 1

Solution:

Suppose surface of water at a depth below the top of the trapezoidal is x meter.

So, approximate Volume of water= (3×2)*dx =6*dx (meter)^3

Since, water weights 1000kg/m^3 .

It follows approximate weight of a representative water , which is also approximate force the pump must extent to move the water is

F(water) = 1000× 6(dx) Newton.

Work to move a representative water is given by

W = 1000*6(dx)*x

We sum the work required to move water through the tank (from x=0 to 6 meter) ,

Work done =integration from x=0 to 6 {1000*6*(dx)*x}=1.08×10^5 N–m

Hence, work needed to pump all water through out tank is 1.08×10^5 N-m