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?
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.