Q.

A liquid density given  by ρ=ρ0[1+αy] is stored in a container, where y is the distance from the top of the liquid surface and  α=23m1.   ρ0 is the density of liquid at the top level. A very small hole is made at the bottom of the container. Find nearest integer value of velocity of efflux (in m/s) when the liquid height is 1 m (assume flow is stream line and  g=10m/s2)

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answer is 4.

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Detailed Solution

12×5ρ03×v2=01ρ0(1+2g3)gydy             5ρ0v26=ρ0g×43           v0=24g15=4m/s

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