Question

Consider a trough with triangular ends where the tank is 10 feet long, top is 5 feet wide, and the tank is 4 feet deep. Say that the trough is full to within 1 foot of the top with water of weight density 62.4 pounds/ft^3, and pump is used to empty the tank until the water remaining in the tank is 1 foot deep. Find the total work to accomplish the task.

Answer 1

at height y from the bottom, the area of the surface of the water is (5/4)y*10 ft^2

So, the weight of a thin layer of water at that height is (5/4)y*10*dy *62.4 = 780y dy lbs

So, the work to lift all the sheets of water at height y is

∫[1,3] 780y(4-y) dy = 5720 ft-lbs