# Homework Help: Object in equilibrium between 2 fluids

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1. Feb 4, 2016

### Epiclightning

1. The problem statement, all variables and given/known data
if an object is in equilibrium at the interface of 2 fluids in an open tank, why do both provide upthrust?

2. Relevant equations
P=P' +dgh

3. The attempt at a solution
The upper fluid is not in contact with the lower part of the object, so why would the fluid provide an upward buoyant force? There is no area at which the fluid could exert a force.
Yet almost all the questions I have seen that deal with such a principle equate mg with the buoyant force due to the lower and upper liquids.

2. Feb 4, 2016

### CrazyNinja

Find the pressure at the lower end of the block and you will understand where you are going wrong.

3. Feb 4, 2016

### Epiclightning

That would be P0 + h1d1g + h2d2g + (h1+h2)(dobjectg), right?

h1, h2 = heights of object in each liquid
d1, d2 = their densities
but how would this simplification help further?

4. Feb 4, 2016

### Staff: Mentor

The pressure on the top of the block is P0.

The pressure on the bottom of the block is P0 + h1d1g + h2d2g

The difference in pressure between the bottom of the block and the top of the block is h1d1g + h2d2g.
So the force is A(h1d1g + h2d2g)=V1d1g+V2d2g. But this is just equal to the sum of the weights of the displaced fluids.

5. Feb 4, 2016

### Epiclightning

So we don't include the weight of the block when we write the pressure?

6. Feb 4, 2016

### CrazyNinja

No you don't.