I am just thinking about this phenomenon: We have a horizontal pipeline with a flowing liquid, which contains a small bubble of gas. How do the dimensions of this bubble change when it reaches a narrower point of the pipeline? Are there practical applications that track bubble sizes to estimate the properties of the flow?
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$\begingroup$ Probably assuming also that the bubble does not split into smaller bubbles right? $\endgroup$– cinicoCommented Sep 2, 2013 at 19:06
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$\begingroup$ Related Meta question: meta.physics.stackexchange.com/q/4940/2451 $\endgroup$– Qmechanic ♦Commented Sep 14, 2013 at 12:48
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1 Answer
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The bubble will get bigger. This is because in a pipe, when you look at a cross-section the same amount of liquid will flow through in a certain amount of time, even if it widens or narrows. This means that current must speed up at narrow points. Bernoulli's principle states that when a fluid increases speed, its pressure decreases. This means that, when the pipe narrows, less pressure is exerted on the bubble. For an ideal gas, $P_1V_1 = P_2V_2$.This means that the bubble must get bigger in the narrow pipe. The praticle application of this is that if we know the volume of a bubble and the pressure that is exerted on it, we can find the pressure on it later by looking at its volume later.
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$\begingroup$ This answer illustrates the concept well enough, though it would be helpful if you incorporated the Laplace pressure to explain more fully. $\endgroup$ Commented May 3, 2015 at 19:01
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$\begingroup$ Do the bubbles travel with the same speed as the fluid? $\endgroup$ Commented Apr 21, 2021 at 7:42