Buoyancy problem in two liquids

[altamashghazi]

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

 

[Doc Al]

What do you think?

 

[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.

 

[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.

 

[altamashghazi]

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.

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.
right answer comes by this.

 

[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.

 

[altamashghazi]

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.

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

 

[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.

 

[altamashghazi]

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.

sorry for that. u r right.