KCET2023PhysicsMechanical Properties of Fluids
A closed water tank has cross-sectional area A . It has a small hole at a depth of h from the free surface of water. The radius of the hole is r so that r A . If p_o is the pressure inside the tank above water level and p_a is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( is density of water)
Options
- Ar^2 2 g h
- Br^2 2 g h+ 2 (p_o-p_a )
- Cr^2 2 g H
- Dr^2 g h+ 2 (p₀-p_a )
Correct answer
B. r^2 2 g h+ 2 (p_o-p_a )
Step-by-step solution
From Bernoulli's principle we have aligned & 1 2 v^2+p₀+ g h= 1 2 v_A^2+p_A+ g(0) & p₀-p_A+ g h= 1 2 v_A^2- 1 2 v^2 & v^2= 2 (p₀-p_A ) + 2 g h P & v= 2 (p₀-p_A ) +2 g h ( v=0 at top ) & Water coming out of hole = area velocity & = r^2 2 g h+ 2 (p₀-p_A ) aligned