# Buoyancy problem in two liquids

1. Mar 4, 2012

### altamashghazi

in attached fig. is their any buoyant force on block by liquid 'A'?what is total force on block by liquid 'A'?

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2. Mar 4, 2012

### Staff: Mentor

What do you think?

3. Mar 5, 2012

### altamashghazi

i think their should not be any buoyant force by 'a'. i mean buoyant force to be vertical and block is not vertically in contact with 'a', so no buoyant force.

4. Mar 5, 2012

### schliere

Think of it this way: at every point in any stationary liquid, there is hydrostatic pressure which is a function of the density of the fluid and the depth into the liquid. There is a force exerted on the block due to fluid "A", but it is inward and balances out because it is acting all along the surface area of the block that is in contact with it. At the bottom of the block, there is pressure upward on the block -- this is the only thing that matters since it is the only place the forces of pressure due to the liquid do not cancel out. This force due to pressure on the bottom face is balanced out (assuming the block is stationary) by the gravitational forces acting on the block.

5. Mar 5, 2012

### altamashghazi

so u say no buoyant force acts on it by 'a'.but if i have to find height of block in air what should i do?
density of block and liquids is given.length of block in 'a' &'b' is given.

i thought of equating buoyant forces on block by "a" &"b" by its weight.

6. Mar 5, 2012

### schliere

To find the pressure on the bottom of the block:

$p_{\text{bottom}}=\rho _A g h_A+\rho _Bg h_B$

where $h_A$ is the height of liquid A and $h_B$ is the height of liquid B

Then, as a force,

$F_{\text{bottom}}=p_{\text{bottom}} * A_{\text{bottom}}$

But this should be self-explanatory.

7. Mar 5, 2012

### altamashghazi

correct correct. yeah. i did so and got the answer . thank u for this concept.

8. Mar 5, 2012

### schliere

To my knowledge, that is the most logical method. I think perhaps if you could want more than that, you don't quite understand fluid statics and should read your textbook.

9. Mar 5, 2012

### altamashghazi

sorry for that. u r right.