Question

2. A tank, initially empty, is in the form of a right circular cylinder with hemispherical ends. The overall

length of the cylinder tank is 3 meters and the diameter of the hemisphere is 1 meter. If a pump

discharges a fluid, whose density is 1.2 kgm/Liter, in this tank at a rate of 300 liters per minute

determine a.) Weight of liquid inside the tank after 5 minutes, KN, and b) total time to fill the tank,

min.

Answer 1

Volume of hemisphere

$V=\frac{1}{2}\frac{4}{3}\pi\frac{d^3}{8}=\frac{\pi d^3}{12}$

Volume of the right circular cylinder

$V_2=\pi\frac{d^2}{4}(l-2\times\frac{d}{2})=\frac{\pi d^2}{8}(l-d)$

$M=\rho(V_1+V_2)$

Put value

$M=550\pi kg m$

$M=1728kg$

Find the mass of liquid inside the tank if it is half full.

$W=mg$

$$W=550\times3.14\times9.8=16950N$$

$V=\frac{\pi d^2}{6}$

Volume

$V=2V_1+V_2$

Put value

$V=\frac{13\pi}{24}m^3$

Now time

$t=\frac{\frac{13\pi}{24}}{0.3}=5.6min$