The density of liquid contained in the tank of area `0.5 m^2` is `1200 kg//m^2`. It has a hole of area `1 cm^2` near the bottom. A load of `30 g` is applied on the liquid at the top. Find the velocity of efflux when the height of liquid level is `75 cm` above the bottom. Take `g = 10 m//s^2`.

Explanation

`a = 1 cm^2, A = 0.5 m^2 = 0.5 xx 10^4 cm^2`
Applying continuity equation
`AV = av`
`V = (a)/(A) v`
Since `a lt lt A, V lt lt v, V^2` is negligible
Pressure at `①`
`P_1 = P_0 + (mg)/(A) = P_0 + (30 xx 10)/(0.5) = P_0 + 600`
Pressure at `②`
`P_2 = P_0`
`P_0` : atmospheric Pressure
Applying Bernoulli's equation between `①` and `②`
`P_1 + rho gh + (1)/(2) rho V^2 = P_2 +(1)/(2) rho v^2`
`V^2` is negligible
`P_0 + 600 + 1200 xx 10 xx 0.75 = P_0 + (1)/(2) xx 1200 v^2`
`600 v^2 = 9600`
`v^2 = 16`
`v = 4 m//s`.
.