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Q.

Consider a uniform cross-sectional closed vessel with its lower part filled with incompressible and non viscous liquid of density ‘d’ up to height ‘9h’ and upper part filled with ideal monoatomic gas to a height ‘h’. The liquid and gas are separated by a movable insulating massless piston. Assume that initial pressure of the gas is 32 P0, where  P0 is the atmospheric pressure. There is an orifice at the bottom of the vessel. If the gas expands adiabatically to a length 8h. Then the instantaneous efflux velocity of the liquid is xhg  The value of x is (g is the acceleration due to gravity).

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answer is 4.

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Detailed Solution

In adiabatic process  P1V1γ=P2V2γ

32P0(Ah)5/3=P1(A.8h)5/3 P1=P0

Apply Bernoulli’s theorem at orifice level

[P0+2hdg]+0+0=P0+12dV2 V=4hg

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