Assertion (A): The speed of efflux of a liquid through an orifice at depth h below the surface is v = 2 g h Reason (R): According to Bernoulli's equation, P + 2 1 ρ v 2 + ρ g h = constant and

Question

Assertion (A): The speed of efflux of a liquid through an orifice at depth h below the surface is v = 2 g h ​ Reason (R): According to Bernoulli's equation, P + 2 1 ​ ρ v 2 + ρ g h = constant and by neglecting air pressure difference and viscosity, v ∝ h ​

TestHub · Accepted Answer

The speed of efflux of a liquid through an orifice at a depth $h$ below the free surface is given by Torricelli's law as $v = 2 g h$ . Thus, Assertion (A) is true.

This result is derived using Bernoulli's equation, $P + \frac{1}{2} ρ v^{2} + ρ g h = constant$ . Applying this between the free surface of the liquid and the orifice, and assuming the pressure at both points is atmospheric (neglecting air pressure difference) and the fluid is non-viscous, we get:

$P_{a t m} + 0 + ρ g h = P_{a t m} + \frac{1}{2} ρ v^{2} + 0$

$ρ g h = \frac{1}{2} ρ v^{2} \Rightarrow v = 2 g h$

From this, it is clear that $v \propto h$ . Thus, Reason (R) is true and correctly explains Assertion (A).

Answer: Both A and R are true, and R is the correct explanation of A

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