Question

State and prove Torricelli’s theorem.

Solution

Torricelli's Theorem states that the velocity of efflux of the liquid through an orifice is equal to the velocity which a body would attain in free fall from the surface of liquid to orifice.

Proof:
Consider a tank containing an ideal liquid of density ρ and having a narrow orifice at L.
Let the tank be very wide as compared to orifice so that velocity of its free surface can be taken zero.
Let v be velocity of efflux.
The pressure at free surface M of liquid and at orifice L is atmospheric.
i.e., P and let h be the height of liquid above orifice.
Applying Bernoulli's theorem at L and M,

space space space space space space straight P subscript straight L over straight rho space plus space gh subscript straight L space plus space 1 half straight v subscript straight L squared space equals space straight P subscript straight M over straight rho space plus space gh subscript straight M space plus space 1 half straight v subscript straight M to the power of 2 space end exponent rightwards double arrow fraction numerator straight P subscript straight L space minus space straight P subscript straight M over denominator straight rho end fraction space plus space space 1 half open parentheses straight v subscript straight L squared space minus straight v subscript straight M to the power of 2 space end exponent space close parentheses space equals space straight g open parentheses straight h subscript straight M space minus straight h subscript straight L space close parentheses space rightwards double arrow space 0 space plus space space 1 half straight v squared space equals space gh space rightwards double arrow space straight v space equals space square root of 2 gh end root space When space straight a space body space falls space freely space by space height space straight h it apostrophe straight s space velocity space straight v apostrophe space is comma space straight v space equals space square root of 2 gh end root space

Hence velocity of efflux of liquid is equal to velocity of free falling body.

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Mechanical Properties Of Fluids

State and prove Torricelli’s theorem.

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What is the SI unit of pressure?

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