Water in a cylinder of height 12 ft and radius 3 ft is to be pumped out.

Question

The density of water is 62.4 lb/ft^3. Find the work required if?

 

(a) The tank is full of water and the water is to be pumped over the top of the tank.

Work =
(include units)

(b) The tank is full of water and the water must be pumped to a height 5 ft above the top of the tank.

Work =
(include units)

(c) The depth of water in the tank is 6 ft and the water must be pumped over the top of the tank.

Work =
(include units)  

 

Answer 1

(a)

The Height of the cylinder is 12 ft.

Radius of the cylinder is 3 ft.

Work = Weight of the cylinder * Height of the water to be raised.

Weight is given by volume * density.

Therefore Work = (volume of the cylinder) * Density of water * Height of the water to be raised.

Now to pump the water to the full of tank then integrate the above from 0 to 12.

Therefore the Work required to fill the tank is 127,030.92.

Answer 2

(b)

The Height of the cylinder is 12 ft.

Radius of the cylinder is 3 ft.

Work = Weight of the cylinder * Height of the water to be raised.

Weight is given by volume * density.

Therefore Work = (volume of the cylinder) * Density of water * Height of the water to be raised.

Now to pump the water to the full of tank and water to be pumped 5ft above the top of the tank.

Total height  = (12 + 5) = 17.

Therefore the Work required to fill the tank and 5 ft above the tank is 127,030.92 ft-lb.

Answer 3

(c)

The Height of the cylinder is 12 ft.

Radius of the cylinder is 3 ft.

Work = Weight of the cylinder * Height of the water to be raised.

Weight is given by volume * density.

Therefore Work = (volume of the cylinder) * Density of water * Height of the water to be raised.

Depth of the water in the tank is 6ft and the water must be pumped over the top of the tank.

Remaining Height for which water to be filled is 12-6 = 6

Therefore the Work required to fill the tank and 5 ft above the tank is 95,273.19 ft-lb.