# Buoyancy problem in two liquids

• altamashghazi
In summary, the expert explains that there is no buoyant force on the block by fluid A because the pressure exerted by the fluid is balanced out by the gravitational forces and the block is not vertically in contact with the fluid. To find the height of the block in air, the pressure on the bottom of the block can be calculated by adding the pressures from fluids A and B. This pressure can then be used to calculate the force on the bottom of the block. The expert also suggests reading a textbook for a better understanding of fluid statics.
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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What do you think?

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.

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.

schliere said:
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.

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.

schliere said:
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.

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.

schliere said:
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.

## 1. What is buoyancy?

Buoyancy is the upward force exerted by a fluid on an object immersed in it, which is equal to the weight of the fluid displaced by the object.

## 2. How does buoyancy work in two liquids?

In two liquids, the buoyant force is determined by the difference in densities between the two liquids and the volume of the object submerged in each liquid. The object will float if the buoyant force is greater than its weight and sink if the buoyant force is less than its weight.

## 3. What factors affect buoyancy in two liquids?

The density of the liquids, the density of the object, and the volume of the object submerged in each liquid all affect the buoyant force in two liquids. Additionally, the gravitational force and the weight of the object also play a role.

## 4. How does Archimedes' principle relate to buoyancy in two liquids?

Archimedes' principle states that the buoyant force on an object is equal to the weight of the fluid it displaces. This principle applies to buoyancy in two liquids as well, where the buoyant force is determined by the difference in densities between the two liquids and the volume of the object submerged in each liquid.

## 5. How can we calculate buoyancy in two liquids?

To calculate the buoyant force in two liquids, we can use the formula Fb = (ρ2 – ρ1) * V * g, where ρ2 is the density of the lower liquid, ρ1 is the density of the upper liquid, V is the volume of the object submerged in each liquid, and g is the acceleration due to gravity. This formula assumes that the object is completely submerged in both liquids.

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