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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

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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 = \( \sqrt{2g{p - p_0)\over rhog}} = \sqrt{{2p - p_0)\over \rho}} \)

=\(\sqrt{\frac{2(4\times 10^5)}{10^3}}=20\sqrt2\) =28.28 m/s

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