Question

A​ right-circular cylindrical tank of height 8 ft and radius 4 ft is laying horizontally and is full of fuel weighing 52 ​lb/ft3. How much work is required to pump all of the fuel to a point 13 ft above the top of the​ tank?

Answer 1

Given:

Height of tank = 8 ft

and we need to pump fuel weighing 52 lb/
`ft^(3)` to a height of 13 ft above the tank top

Solution:

Total height = 8+13 =21 ft

pumping dist = 21 - y

Area of cross-section =
`\pi r^(2)` =
`\pi 4^(2)` =16
`\pi`
`ft^(2)`

Now,

Work done required =
`\int_(0)^(8) 52* 16\pi (21 - y)dy`

=
`832\pi \int_(0)^(8) (21 - y)dy`

= 832
`\pi(`
`[ 21y ]_(0)^(8) - [(y^(2))/(2)]_(0)^(8)\\`)

= 113152
`\pi` = 355477 ft-lb

Therefore work required to pump the fuel is 355477 ft-lb