A wide vessel with small hole in the bottom is filled with water and kerosence, Neglecting viscosity, the velocity of water flow v, if the thickness of water laer is `H_(1)` and that of kerosene layer is `H_(2)` is (density of water `P_(1)g//cc` and that of kerosene is `P_(2)g//cc`.

Options

A. `v=sqrt(2g(h_(1)+h_(2)))`
B. `v=sqrt(2g(h_(1)p_(1)+h_(2)p_(2)))`
C. `v=sqrt(2g[h_(1)+h_(2)((p_(2))/(p_(2)))+h_(2)])`
D. `v=sqrt(2g[h_(1)((p_(1))/(p_(2)))+h_(2)])`

Answer

C

Explanation

Applying bernoulis theorem for point 1 and 2
`p_(1)gh_(1)+p_(2)gh_(2)+(1)/(2)pv^(2)+P_(0)`
`=0+(1)/(2)p_(1)v^(2)+P_(0)(vltltv^(2))`
`p_(1)gh_(1)+p_(2)gh_(2)=(1)/(2)p_(1)v^(2)`

`v=sqrt(2g[h_(1)+h_(2)((p_(2))/(p_(1)))])`