Using Integration and ftlbs A spherical tank 24 feet in diam

Using Integration and ft/lbs:

A spherical tank, 24 feet in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long will it take to fill the tank? (One horsepower= 550 ft/lb of work per second).

Solution

the volume is calculated as follows:

   V = (4/3)*pi*r^3 = (4/3)*pi*(24 /2)^3 = 7238.23 ft^3 = 205 m^3

height of center of tank is,

h = 60+12 = 72 ft = 22 m

work done is,

   W = mgh = pVgh = 1000*205*9.8*22 = 4.4198e+7 J

Total work done by pump is,

   W = Pt = 1.5 hP * t = 1.5 * 2684519.54 *t

hence, the time t is,

   1.5 * 2684519.54 *t = 4.4198e+7 J

                                 t = 1.749 hr

                                   = 104.95 min

                                   = 6296.4 s