2019 Mechanical Properties of FluidsBernoulli's Principle – Speed of Efflux (Torricelli's Law) Medium Question 21 of 34 in Mechanical Properties of Fluids

A small hole of area of cross-section $2\ mm^2$ is present near the bottom of a fully filled open tank of height 2 m. Taking $g=10\ m/s^2$, the rate of flow of water through the open hole would be nearly:

A $12.6\times10^{-6}\ m^3/s$
B $8.9\times10^{-6}\ m^3/s$
C $2.23\times10^{-6}\ m^3/s$
D $6.4\times10^{-6}\ m^3/s$

The answer is A.

Solution

Velocity of efflux: $u=\sqrt{2gh}$ Rate of flow $Q=au=a\sqrt{2gh}$ $Q=2\times10^{-6}\times\sqrt{2\times10\times2}\ m^3/s=2\times10^{-6}\times2\sqrt{10}$ $=2\times2\times3.14\times10^{-6}=12.56\times10^{-6}\ m^3/s$ $Q\approx12.6\times10^{-6}\ m^3/s$

Concept rate of flow through a hole in a tank

Mechanical Properties of Fluids in past papers

34 questions from this chapter have appeared across 14 exam years.