A cylindrical tank with a large diameter is filled with water. Water drains out through a hole at a bottom of the tank . If the cross - sectional area of the hole is `6 cm ^2` then the drainge rate ( in `m^3//s`) when the depth of the water is 0.2 m is

Options

A. `1.0 xx 10^(-3)`
B. `8.2 xx 10^(-2)`
C. `22 xx 10^(-3)`
D. `1.2 xx 10^(-3)`

Answer

D

Explanation

Given cross - section area of hole
`A = 6xx 10^(-4) m^2` and depth of the water , h= 0.2 m
From torricell's thorem ,
Velocity of water , `v= sqrt(2gh)`
`rArr v= sqrt(2 xx 10 xx 0.2 ) = 2 m//s`
Now, from equation of continuity, Av = drainage rate
`rArr` Drainage rate =` 2 xx 6xx 10^(-4) = 1.2 xx 10^(-3) m^3 //s`