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 = $\int_{0}^{8} 52\times 16\pi (21 - y)dy$

                                  = $832\pi \int_{0}^{8} (21 - y)dy$

                                  = 832$\pi($$[ 21y ]_{0}^{8} - [\frac{y^{2}}{2}]_{0}^{8}$)

                                  = 113152$\pi$ = 355477 ft-lb

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