Question

With what velocity does water flow out of an orifice in a tank with gauge pressure 4x10⁵ N/m² before the flow starts? Density of water = 1000 kg/m³

Answer 1

Correct answer= 28.28 m/s

Explaination

Given:: p - p₀ = 4 × 10⁵ Pa, ρ = 10³ kg/m³

If the orifice is at a depth h from the water surface in a tank, the gauge pressure there is

p - p₀ = hρg         ....(1)

By Toricelli’s law of efflux, the velocity of efflux,

v = $\sqrt{2gh}$      ...(2)

Substituting for h from Eq.(1),

v = $\sqrt{2g\frac{p-p_0)}{rhog}}=\sqrt{\frac{2p-p_0)}{\rho }}$

=$\sqrt{\frac{2(4\times {10}^5)}{{10}^3}}=20\sqrt{2}$ =28.28 m/s