# Why do the bubbles in the water cooler get larger as the level gets lower?

I have a typical office water cooler that uses a 19 liter bottle as a reservoir. The bottle is inverted on the base of the cooler with its neck below the water level in the cooler's reservoir. Air pressure (or more precisely, the reduced pressure above the water in the bottle) stops the water from flowing out once the level in the cooler's base reaches the bottle's neck.

I have noticed that the size of the bubbles that enter the bottle as water is withdrawn is inversely proportional to the head (height of water in the bottle). For example, when the bottle is full of water (head ~50cm) it takes about 100 bubbles to fill the jug I use to collect the water. When the bottle is almost empty (head ~ 15cm) it takes only 20 bubbles to fill the same jug. The smaller bubbles when the bottle is full also enter faster (i.e. more frequently) but take longer, that is they continue for a longer period after I close the valve when filling my jug.

I am at a loss to understand the physics behind this phenomenon.

Water will run out of the bottle (and bubbles enter to replace the volume lost) until the water level in the reservoir (basically a bucket with a valve at the base) reaches the neck of the bottle inverted into it which prevents further air from entering. Water is then removed from the reservoir by opening the valve. This lowers the water level in the reservoir below the mouth of the bottle which allows more air to bubble in and water to flow out until the level again reaches the neck of the bottle. As the air is being drawn in at atmospheric pressure I am confused by the changing size and frequency of the bubbles.

Here is a schematic drawing of the apparatus (apologies for the lousy drawing skills).

• This video shows that the inner working of the water cooler is somewhat intricate. The video explains partially how the bubbles are formed near the neck of the bottle. youtube.com/watch?v=RlXVm6WH2J8 – Ján Lalinský Sep 20 '18 at 19:26
• Does the top surface of the bottle "oil can" at any point--pop in and out? It seems possible that as the level gets lower and there is a smaller pressure differential across this surface, it might start to do this, allowing it to slurp more air at a time. Just a thought. – Ben51 Sep 26 '18 at 1:24

This is most likely just the ideal gas law at work.

As you move deeper into a fluid, the pressure is given by $$P=\rho gh$$

Where $\rho$ is the fluid density, $g$ is the acceleration due to gravity, and $h$ is the depth into the fluid.

According to the ideal gas law $$V=\frac{nRT}{P}=\frac{nRT}{\rho gh}$$

As you can see, the volume and the water level are inversely related. A lower water level means a larger volume.

Qualitatively, when the water level is lower, there is less pressure to push on the bubbles, so they are able to expand to a larger size.

Therefore, for the same amount of water that leaves the cooler (which means the same amount of air enters the cooler), when the water level is higher, the amount of air that comes in is divided into smaller bubbles, giving a higher frequency of bubbles. At lower water levels, the same amount of air gets divided into fewer, larger bubbles at a smaller frequency. I believe that the water pressure at the bottom of the cooler also contributes to this, as a larger pressure will "cut off" the bubble formation due to larger forces at the base of the bubbles.

I am unsure about the continuation of bubbles after the valve has closed. It could just be the time it takes for air to flow to the water portion of the cooler, and the rate of air flow could depend on the water level as well. Also, perhaps there is some way the cooler operates to purposefully take in air a certain way that I am unaware of. Have you looked into the inner workings of the cooler?

• I'm still unsure that I understand. The air pressure at the top of the bottle is less than atmospheric pressure by the amount required to support the level in the bottle. The bubbles that enter the bottle would do so at atmospheric pressure when the level in the reservoir drops below the mouth of the bottle. This does not explain why more and smaller bubbles are required when the head is high than when the head is low. – Frowie Sep 19 '18 at 18:52
• "@Aaron Stevens" I have added a picture of a typical cooler to the question. Intuitively, it seems to me that there should be a partial vacuum above the water in the bottle but I may be wrong about that. What really confuses me is why it takes about 100 bubbles of air to extract about 2 litres of water when the bottle is full (i.e. high head) versus 20 bubbles for 2 litres when the bottle is nearly empty (i.e. low head). – Frowie Sep 19 '18 at 20:33
• I have not recorded the time to fill although it seems roughly similar in both cases. I suspect that velocity through the outlet valve as the constraining factor is similar hence time would be. The rate at which the bubbles form is different. Although total time is the same, high head = fewer, larger bubbles at a slower rate while low head = more, smaller bubbles at a more frequent rate. In the low head case the bubbles continue after the valve is closed for a longer time than in the high head case. – Frowie Sep 19 '18 at 21:43
• @Frowie I have added some more information. I am not completely sure about my answer though. Perhaps looking into how the cooler actually operates would help reveal some information. For example, if the cooler is designed in a certain way to let in air in a specific way, this could help shed some light on all of this. – Aaron Stevens Sep 20 '18 at 11:21
• I have added some more information and a conceptual schematic drawing to better describe the system. – Frowie Sep 20 '18 at 15:38