A cylindrical tank of area 5m^2 contains water filled to a height

a-cylindrical-tank-of-area-5m-2-contains-water-filled-to-a-height

A cylindrical tank of area 5m^2 contains water filled to a height of 10cm. A hole of area 0.005m^2 is present at the bottom. What is the time required for the water level to become half?

A. 100s

B. 10s

C. 1min

D. 10min

I got this question in an online interview.

The question is from Fluids Mechanical Properties in section Mechanical Properties of Fluids of Physics – Class 11

Right option is A. 100s

Explanation: The speed of efflux when height of water is ’h’ = \(\sqrt{2gh}\).                                                                           The volume of water flowing out in time dt is Avdt = 0.005*\(\sqrt{2gh}\)*dt.                                                              Therefore the decrease in height of water level (dh) in time dt is vol flowing out / area of tank                        = 0.005\(\sqrt{2gh}\)dt/5.

dh = \(\sqrt{2gh}\) (0.005)dt/5

\(\int_{0}^{0.05}dh/\sqrt{h} = \int_{0}^{t}\sqrt{2g}\)0.001 dt

∴ 2\(\sqrt{0.05}\) = \(\sqrt{20}\)0.001 t

∴ t = \(\sqrt{0.2}\)*1000/\(\sqrt{20}\) = 100s.