Bubble Mumble

Classical Mechanics Level 1

When a goldfish puffs out an equal amount of air each time he mumbles under water, how do the bubbles form?

A. The bubbles gradually get larger as they get closer to the surface.
B. The bubbles always stay the same size throughout the ascent.
C. The bubbles gradually shrink as they reach the surface.
D. None of the above. The bubbles will randomly vary in size.

A B C D

7 solutions

Worranat Pakornrat
Mar 14, 2017

As we dive in under water, the water pressure will increase directly to the depth descended. Approximately, by diving down $10$ meters will increase the pressure by $1$ atmosphere: the pressure acting upon us will be doubled at $10$ meters depth.

As such, the air at deeper depth will be more compressed and, thus, smaller in size, compared to the surface, but when it rises, the air will be "decompressed" and can have more occupying space, expanding gradually during its ascent.

Therefore, the bubbles will get larger and larger as they rise up to the surface.

Note : During diving, it is forewarned not to ascend faster than the bubbles themselves. Otherwise, the air bubbles inside the diver's body will "decompress" and expand to the point that it causes muscle pain and even blocking small vessels. This type of condition is called Caisson's Disease , also known as "decompression sickness", and affected patients would need to undergo hyperbaric chamber treatment, where the air environment is mimicked to be pressurized as if it were under water in order to "recompress" those air bubbles. This must be supervised by the specialists and slowly tapered so the body can adapt to normal pressure again.

It would work better with a creature which actually does exhale bubbles under water.

Marta Reece - 4 years, 2 months ago

Yes, I was thinking of a whale though my drawing skills were not that great. :p

Worranat Pakornrat - 4 years, 2 months ago

I love your drawings.

Marta Reece - 4 years, 2 months ago

Whales don't exhale through the mouth. They don't exhale under water either :)

Florin Ilia - 4 years, 2 months ago

Actually, they do. Blow hole may be more a nose than a mouth, but they do exhale under water when they use walls of bubbles to hunt fish.

Marta Reece - 4 years, 2 months ago

The problem stated that a goldfish puffs out bubbles, so, in a domestic aquarium. We are not talking about a whale in deep open sea. So, in an aquarium, there is no deep to make this effect visible and the answer should be B. I dare anyone could prove the bubbles grow as it rise, in a domestic aquarium.

Miguel Rozsas - 4 years, 2 months ago

Well theoretically, under the isothermal conditions, the bubbles will grow in size with rising even in an aquarium. Although, if the aquarium is small then the change in the size will be very small may be beyond measurement.

Rohit Gupta - 4 years, 2 months ago

What if the air temperature drops due to surrounding water...then it should compress. Has temperature not been considered?

Karan Gujarathi - 4 years, 2 months ago

Goldfish are coldblooded. They are the same temperature as the surrounding water.

Marta Reece - 4 years, 2 months ago

Mac A
Mar 28, 2017

P1V1 = P2V2 (assuming temperature to be approximately constant) As bubble rises up, the pressure decreases hence volume has to increase correspondingly.

What if we don't consider a constant temperature? Suppose, it is a hot summer day, will the bubbles will still grow in size?

Rohit Gupta - 4 years, 2 months ago

Joy Patel
Mar 27, 2017

Water pressure is directly proportional to depth.

Poorly designed problem. Yes, theoretically the size of the bubbles will increase BUT ONLY for a significant difference in pressure. At the scale the problem is presented there WILL be more variations in the size of the bubbles due to the randomness of how the bubbles are produced

Javier Guevara - 4 years, 2 months ago

The question restricts the randomness by stating that goldfish puffs out an equal amount of air each time to form a bubble. Yes, I agree practically the change in the size of the bubbles will be very small and the options also agree to this fact as they mention the size will gradually increase. However, sometimes small changes may cause big problems. As Worranat had already talked about it in his solution, let me restate it here again.

"During diving, it is forewarned not to ascend faster than the bubbles themselves. Otherwise, the air bubbles inside the diver's body will "decompress" and expand to the point that it causes muscle pain and even blocking small vessels. This type of condition is called Caisson's Disease, also known as decompression sickness".

Rohit Gupta - 4 years, 2 months ago

Aditya Kumar
Apr 2, 2017

By fluid mechanics, The pressure difference outside and inside the bubble is given by p = 4S/R ( Where, S= surface tension, R= radius of bubble). We can clearly see, p is inversely proportional to R. Which will mean that as pressure decrease, radius increases. Also, the the pressure increases with depth as , p = DgH ( d= density, g = accl. Due to gravity,h= height). Hence, Radius will increase.

Swabhiman Nayak
May 15, 2017

As the bubble goes up the pressure decreases and the size increase..

A Former Brilliant Member
Apr 18, 2017

Gas easily respond to pressure change via its volume. Towards way to surface of bubble it experience pressure decrease and thus volume of bubble increase presuming nothing dramatic happens to temperature of water. Proof: Boyle's law PV=constant at given Temp for gases

Arjun Singh
Mar 29, 2017

Relevant wiki: Boyle's Law

By Boyle's law, pressure and volume are inversely related, with the equation P1V1=P2V2. As pressure decreases, while the bubble rises, the volume of the bubble will increase.

To add to the solution, the pressure inside water increases with depth. As the bubble rises it moves from a high-pressure region to a low-pressure region. Thus, due to the fall of external pressure, the pressure inside the bubble push on its wall to increse its size.

Rohit Gupta - 4 years, 2 months ago

Bubble Mumble

7 solutions

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