Bernoulli’s Theorem and its Application – Rankers Physics
Topic: Solid and Fluids
Subtopic: Fluid Dynamics

Bernoulli’s Theorem and its Application

A small hole of area of cross-section $2 \text{ mm}^2$ is present near the bottom of a fully filled open tank of height $2 \text{ m}$. Taking $g = 10 \text{ m/s}^2$, the rate of flow of water through the open hole would be nearly

(2019)

$12.6 \times 10^{-6} \text{ m}^3/\text{s}$
$8.9 \times 10^{-6} \text{ m}^3/\text{s}$
$2.23 \times 10^{-6} \text{ m}^3/\text{s}$
$6.4 \times 10^{-6} \text{ m}^3/\text{s}$

Solution:

Velocity of efflux is $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 2} = \sqrt{40} \text{ m/s}$. The rate of flow is given by $Q = Av = 2 \times 10^{-6} \times \sqrt{40} \approx 12.64 \times 10^{-6} \text{ m}^3/\text{s}$.

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