# Homework Help: Speed of Efflux

1. Sep 28, 2010

### zorro

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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?

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2. Sep 28, 2010

### 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.

Last edited: Sep 29, 2010
3. Sep 29, 2010

### zorro

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

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

4. Sep 29, 2010

### rl.bhat

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

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.

5. Sep 29, 2010

### zorro

Thanks alot, Sir.