# The acceleration of a bubble in water

• Istvan01
In summary, the conversation was about the initial acceleration of a bubble in water, which was stated to be 2g in a reference provided by the person asking the question. The other person questioned the validity of this statement and requested a clear reference for it. The referenced source was found to only explain the 2g acceleration in certain conditions and did not provide a clear explanation for it. Further references were suggested for better understanding.

#### Istvan01

Hi,

I have a question about a rising bubble.
I read that the initial acceleration of a bubble (with negligible mass) in water is 2g, where g is the gravitational acceleration. I understand that if a bubble rise then the water move around it, but I can't derive this equation.
Could someone help me out?

I see no reasonable argument for this statement.
What is your reference and what does it say to justify such a claim ?

Istvan01 said:

This requires a clear reference to the source.

Zz.

Looking at the pdf file, the problem 52 seems to assume that the liquid has no viscosity, which isn't true in general.

I did find a 2g here but don't see an explanation. And here it gets worse: 3.3 g ! But they do show how the 2g comes about in section 2 (of course ). So your derivation is available.

Must admit I learned to be a bit more open-minded: at first I didn't believe more than g is physically possible...

This one below ? I don't see it. But then again: you say the answer is 2. So: follow the steps and see where you end up

#### Attachments

52.8 KB · Views: 512
Thanks, I'm not certain that I can understand your reference because that seems very complicated but I'll try

BvU

## What causes a bubble to accelerate in water?

A bubble accelerates in water due to the difference in density between the gas inside the bubble and the surrounding water. This creates a buoyant force that pushes the bubble upwards, causing it to accelerate.

## Does the size of the bubble affect its acceleration in water?

Yes, the size of the bubble does affect its acceleration in water. Generally, larger bubbles will accelerate more slowly than smaller bubbles due to their larger surface area and higher drag forces.

## What factors can affect the acceleration of a bubble in water?

The acceleration of a bubble in water can be affected by factors such as the size and shape of the bubble, the temperature and pressure of the water, and the presence of any impurities or surfactants in the water.

## Can the acceleration of a bubble in water be calculated?

Yes, the acceleration of a bubble in water can be calculated using the equation a = (ρb - ρw)gV/mb, where a is the acceleration, ρb is the density of the bubble, ρw is the density of the water, g is the acceleration due to gravity, V is the volume of the bubble, and mb is the mass of the bubble.

## How does the acceleration of a bubble in water compare to the acceleration of a bubble in air?

The acceleration of a bubble in water is generally slower than the acceleration of a bubble in air due to the higher density and viscosity of water compared to air. However, the acceleration of a bubble in water can be increased by increasing the temperature or pressure of the water.