Fluids at rest exert a normal force to the walls of the container or to the sruface of the body immersed in the fluid. The pressure exerted by this force at a point inside the liqid is the sum of atmospheric pressure and a factor which depends on the density of the liquid, the acceleration due to gravity and the height of the liquid, above that point. The upthrust acting on a body immersed in a stationary liquid is the net force acting on the body in the upward direction. A number of phenomenon of liquids in motion can be explain by Bernoulli's theorem which relates the pressure, flow speed and height for flow of an ideal incompressible fluid.
A container of large uniform cross sectional area. A resting on a horizontal surface holds two immiscible, non viscous and incompressile liquids of densities `d` and `2d`, each of height `H//2` as shown in the figure. The lower density liquid is open to the atmosphere having pressure `P_(0)`.
Situation II:
A cyliner is removed and the original arrangement is restored.A tiny hole of area `s(slt ltA)` is punched on the veritical sideof the containier at a height `h(hltH//2)`
The initial speed of efflux of the liquid at the hole is

Options

A. `(sqrt((4H-3h)g))/2`
B. `(sqrt((3H-4h)g))/2`
C. `(sqrt((3H-3h)g)/2)`
D. `sqrt((3H-3h)g/2)`

Answer

D

Explanation

Pressure at hole, before opening:
`P=P_0+dgH/2+2dg(H/2-h)`
After opening the hole, pressure decreases, and pressure energy converts into KE so,
`P-P_0=1/2(2d)v^2`
`implies dgH/2+2dg(H/2-h)=dv^2`
`impliesv=sqrt(((3H)/2-2h)g)=sqrt(((3H-3H)g)/2)`