Question

Define Torricellis law
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Answer 1

Answer:

Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from an orifice to the height of fluid above the opening. The law states that the speed v of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e. {\displaystyle v={\sqrt {2gh}}}v = \sqrt{2gh}, where g is the acceleration due to gravity (9.81 m/s2 near the surface of the Earth). This expression comes from equating the kinetic energy gained, {\displaystyle {\frac {1}{2}}mv^{2}}\frac{1}{2} mv^2, with the potential energy lost, mgh, and solving for v. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.

Answer 2

Torricelli's Theorem:—

Velocity of efflux from an orifice is equal to velocity of free fall from surface to orifice.

$\rule{200}2$

Proof:—

Applying Bernoulli's theorem on the surface and orifice

P1+1/2pV²1+pgh1= P2+1/2pV²2+pgh2

P+1/2p0²+pgH=P+1/2pV²+pg(H-h)

pgH = 1/2pv²+pgH-pgh

pgh= 1/2pv²

v= √2gh ......(1)

Now,

Velocity of free fall from surface to orifice

v²= u²+2as

v² = 0²+2gh

v=√2gh ...(2)

equation (1) and (2) are identical.

#Hence proved.

$\rule{200}2$