Question

Apply Bernoulli's Principle to determine the speed of efflux
from the side of a container both when its top is closed and open.Hence derive Torricelli's law.​

Answer 1

Explanation:

per the Torricelli’s law for Newtonian fluids, the density of efflux of a fluid passing through a sharp-edged hole at the bottom of a tank filled with the fluid to a depth of h is the same as the speed that a body would acquire in a freely falling condition when falling from a height h.

Derivation

speed of efflux

Consider a tank with a small hole in its side at a height y1 from the bottom, containing a liquid of density ρ. The air above the liquid is at pressure P and its surface is at height y2.

From the equation of continuity, we can write

A1v1 = A2v2

Or v2 = A1v1/A2 ………………………….(1)

If the cross-sectional area of the tank A2 is much larger than that of the hole (A2 >>A1), then we may take the fluid to be approximately at rest at the top, i.e. v2 = 0. Now applying the Bernoulli equation at points 1 and 2 and noting that at the hole P1 = Pa (the atmospheric pressure), we have

Pa + 1/2ρv12+ ρgy1 = Pb + 1/2ρv22 + ρgy2 ……………………………(2)

Here, let the difference in the height = h (as shown in the figure) = y1-y2

From equation 1 and 2, we have

v1=2ρ−−√[(p−pa)+ρgh]

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