A large tank is filled with two immiscible liquids of densities ` rho _ 1 and rho _ 2 ` A small hole is made at the base of the tank and liquid of density ` rho _ 2 ` starts flowing out of it. Three points A, B and C are marked on a vertical line. Velocity with which liquid leaves the hole is :

Options

A. ` sqrt ((g(rho _1h_1 + rho_2 h_2 ))/(rho _2) ) `
B. `sqrt ((2g (rho_1 h_1 + rho_2 h_2 ))/(rho_2 )) `
C. `sqrt ((2g(rho_1h_1 + rho_2 h _ 2 ))/(rho _1 ) ) `
D. `sqrt(2g (h_1 + h_2 ) ) `

Answer

B

Explanation

Liquid pressure at C (just above the hole) ` = P _ C = P _ 0 + (rho _ 1 h_1 + rho_2h _ 2 ) g `
Applying Bernoulli’s between a point jut above the hole and a point just below the hole.
`P_C = P_0 + (1)/(2) rho_2 v^2 rArr v = sqrt((2g (rho _1 h_1 + rho _2 h _ 2 ))/(rho _2 ))`