Finding Speed of Efflux for Two Liquids of Different Densities

[zorro]

Homework Statement

The container of uniform cross section area A holds two immiscible non-viscous incompressible liquids of densities d and 2d each of height H/2. A tiny hole of area S<<A is punched on the vertical side of the container at height h(<H/2)

Find the speed of efflux.

Homework Equations

The Attempt at a Solution

I know how to find it when there is only one liquid present.
What is the approach in this case?

 

[rl.bhat]

The pressure difference at the hole is
P - Po = g[H/2*d + (H/2-h)*2d ]

The density of the liquid flowing out is 2d. Hence the velocity of the liquid is

v = sqrt[2(P - Po)/2d]

Substitute the values and find v.

 

[zorro]

The pressure difference at the hole is
P - Po = g(H/2*d + H/4*2d) = gHd

how did you get H/4*2d? the height 'h' is a variable.

The density of the liquid flowing out is 2d

After some time density of liquid flowing out will be d. But we are not taking it into account. Why is it so?

 

[rl.bhat]

]how did you get H/4*2d?[/B] the height 'h' is a variable.

It should be (H/2 - h)*2d

After some time density of liquid flowing out will be d. But we are not taking it into account. Why is it so?

From the expression we get only the initial velocity. As the level of the liquid decreases, the velocity will also change. When the liquid with density d flows out, again velocity will change.

 

[zorro]

Thanks a lot, Sir.