# Buoyant force when object is between two liquids

Suppose we have a ball floating in liquid A. Then we pour a liquid B on top of the ball (Assuming that the liquid is poured such that the ball doesn't oscillate) . The ball rises up. Why? According to me, the liquid on top (liquid B) will exert a force downward on the ball and it should go lower. The particles in the liquid B will exert an normal force which is acting downwards on the ball. How can adding liquid B make it rise up, that is, provide an upward force?

Taking a specific case, density of B > density of ball > density of A what would happen?

• The result probably means that the ball rises up after pouring the liquid and once it's settled. The exact motion is too complicated to determine upon pouring, and also specification of the density of the fluids and the material of the ball is required. Mar 20, 2019 at 14:10
• @GodotMisogi Even after the liquid has settled, the normal contact force should be downwards right? Mar 20, 2019 at 14:19
• If you have the ball standing at the bottom of a tank and you then pour liquid A over it, then it will also rise. The same thing happens when liquid B is poured - liquid A is the "bottom" this time. Mar 20, 2019 at 14:20
• @Steeven I think that depends on the density of the ball and whether it's larger or smaller than the density of liquid B. Mar 20, 2019 at 14:31
• BTW, was there a typo in this question? I think it should read density A > density of ball > density B, or else the ball wouldn't have been floating in the first place.
– JMac
May 2, 2019 at 19:25

There's a key factor you're missing when you're considering the added weight on the ball.

The fluid B wont just be pushing down on the top of the object floating in liquid A, it also pushes down on liquid A itself. Due to the hydrostatic principle, this therefore increases the pressure of liquid A. This added pressure increases the force that liquid A is exerting on the object in the upwards direction. This is already enough to cancel out the effects of the added weight on top of the object.

As far as the additional height goes, this is because fluid B is more dense than air. Using Archimedes' principle, we can see that this should necessarily increase the buoyant force on the object because $$F_{Buoyant} = \rho_{fluid} V g$$ (where V is volume displaced by the submerged object, $$\rho_{fluid}$$ is the density of the fluid and $$g$$ is acceleration due to gravity.

We can see that when the density of the surrounding fluid increases (and it should be safe to assume fluid B is more dense than the air formerly above fluid A), the buoyant force increases, which will result in more lift on the submerged object. As it rises, the effective density of the fluid will decrease, as more and more of the object gets surrounded by the less dense fluid B, instead of fluid A. (Buoyancy then becomes $$F_{buoyant} = ( \rho_{A} V_{A} + \rho_{B} V_{B} ) g$$ where $$V_A$$ and $$V_B$$ are the volumes that each fluid acts on respectively) If fluid B is more dense than the object, it will continue to rise until it floats on fluid B; if fluid B is less dense than the object, it will rise until $$F_{buoyant} = F_{gravity}$$ and it reaches an equilibrium position between the two fluids.

• Awesome answer sir, and sorry for pinging you a year late. But in one of my questions you said buoyancy can't be used if the same type of liquid is not below it, But you have taken the buoyancy due to oil here sir. Dec 16, 2020 at 13:12
• @JustJohan The big difference between those two situations is that in that other question, the fluid below isn't in contact with the fluid above, so the pressure above can actually be higher than the pressure below. If the object is actually fully surrounded by fluid, they can be different fluids, but there can't be like a container between the two fluids that prevents hydrostatic pressure from building up, in that case Archimedes' Principle goes out the window because its no longer really an object just surrounded by a fluid.
– JMac
Dec 16, 2020 at 15:29
• Thanks a lot sir, I completely get it. Dec 16, 2020 at 15:42