Q: There is a hole at the side-bottom of a big water tank. The area of the hole is 4mm^{2}. Through it a pipe is connected. The upper surface of water is 5 m above the hole. The rate of flow of water through the pipe is (in m³s^{-1}) (g = 10 ms^{-2})

(a) 4 × 10^{-5}

(b) 4 × 10^{5}

(c) 4 × 10^{-6}

(d) 28 × 10^{-5}

Ans: (a)

Sol:

Velocity of efflux is

$ \displaystyle v = \sqrt{2 g h} $

$ \displaystyle = \sqrt{2 \times 10 \times 5} = 10 m/s $

Rate of flow

$ \displaystyle = A v = 4 \times 10^{-6}\times 10 $

= 4 × 10^{-5}