Speaker
Description
The traditional version of the Bernoulli equation assumes the fluid is incompressible and thus realistically it only applies to liquids. However, I will show that it is not hard to modify the derivation so that it applies to compressible gases. This modification is a useful addition in lecture or homework in an introductory calculus-based physics course. I will then show that this modified form fits previously published experimental data [1] on the depressurization of a plastic soda bottle from 3 atm to 1 atm of air through a small hole. An accurate fit [2] requires, however, that the effective size of the hole be reduced compared to its actual size, which makes for a lab experiment motivating the phenomenon of the vena contracta relevant in practical fluid mechanics. I will end with some comments about what one would have to do if the bottle emptied into vacuum (i.e., it depressurizes from 1 atm to zero) rather than into the room, which has application to a manned spacecraft being punctured by a micrometeoroid while in transit to the Moon.
[1] K. Atkin, "The spacecraft decompression problem," Phys. Educ. 59, 015035 (2024).
[2] C.E. Mungan, "Comment on 'The spacecraft decompression problem'," Phys. Educ. 59, 038003 (2024).
