Question

A cylindrical tank of radius 3 ft and height 10 ft stands on a flatform 50 ft high. How much work will be done in filling the tank by pumping water from the ground level?

Answer 1

$\text{Find the volume of the tank:}$

$V = \pi r^2h$

$r = 3ft= 0.9144 m$

$h=10ft = 3.048m$

$V= \pi*0.9144^2*3.048\approx 8m^3$

$\text{Let's calculate the water mass in the tank}$

$m=\rho V= 1000*8 =8000kg$

$\text{Calculate the potential energy of the water in the tank}$

$E_p=mgh_c$

$h_c -\text{height of the center of gravity of the tank }$

$\text{relative to the ground level}$

$h_c= 50+10/2=55ft=16.764m$

$E_p=mgh_c=8000*9.8*16.764=1314 297.6J$

$\text{the potential energy of the same mass of water}$

$\text{at ground level will be 0 since the height is 0}$

$E_{p0}=0$

$W =\Delta P= 1314 297.6J$

$\text{Answer: } 1314 297.6\ J$