Name: Capillary Rise
Uploaded: 2019-07-19
Duration: 10 min 29 s
Description: Have you ever seen what happens to a celery stalk dipped in red-coloured water? We notice that after a day or two, the leaves turn reddish! Let's learn the r...

Question

What is Torricelli's law? Explain how the speed of efflux is determined with an experiment.

Accepted Answer

Torricelli's law: The speed of efflux of a liquid freely falling is directly proportional to the square root of the height at which liquid is falling.

Consider a tank containing a liquid of density $ρ$ with a small hole 1 in its side at a height $y_{1}$ from the bottom as shown in the below figure. The air above the liquid, whose surface is at height $y_{2}$ is at pressure P.

Fig: Torricelli's law

Apply equation of continuity at point 1 and point 2,

$v_{1} A_{1} = v_{2} A_{2}$

$v_{2} = \frac{A_{1}}{A_{2}} v_{1}$

If $A_{2} > > > > A_{1}, v_{2} = 0 m / s$

Now, applying Bernoulli's equation at point 1 and point 2 and nothing that at the hole

$P_{1} = P_{a}$

$P_{a} + \frac{1}{2} ρ {v_{1}}^{2} + ρ g y_{1} = P + ρ g y_{2} Taking, y_{2} - y_{1} = h . we have v_{1} = \sqrt{2 g h + \frac{2 (P - P_{a})}{ρ}}$

When, $P > > > P_{a} and 2 g h v_{1} = \sqrt{2 gh}$

Hence, the speed of a free-falling fluid is directly proportional to the square root of the height.

What is Torricelli's law? Explain how the speed of efflux is determined with an experiment.

Important Questions on Mechanical Properties of Fluids

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