An object is traveling through a tube, in a perfect vacuum, at 300 m/s, with no acceleration. It is not in contact with the surface of the tube (imagine zero gravity or some such).
The tube is then vented ahead of the object, and flooded with air. It takes some time for the tube to fill to a pressure of one atmosphere.
Am I correct in thinking that sound travels more slowly in lower air pressure? If so, would there be a sonic boom as soon as the air is introduced? How dramatically would the object slow down?
This scenario is a possible part of a scene in a story I am writing, and I want to get it right. Any detail about how this system would behave would be appreciated.
The Mach number of an object is porportional to the square root of the temperature of the medium it’s travelling through (for a perfect gas). The equation to determine the Mach number doesn’t require a pressure value. All that is required is the absolute temperature of the medium, the ratio of specific heats and the gas constant for the particular medium.
In your scenario, it would seem that you would have a temperature drop in the air as it enters the tube, which would lower the corresponding Mach number. The speed of sound at STP is 340.9 m/s. If the absolute temperature of the air in the tube dropped substantially below standard temperature, you would (probably) get a shock wave attached to the end of the object and (maybe) a weak bow shock wave developed ahead of the object, until it had slowed enough to drop out of the supersonic/transonic region.
Some aeronautical/aerospace engineer will be along shortly to correct and chastise me, I’m sure.
No, strangely enough it works out that in an ideal gas the speed of sound is dependent only on the temperature. You can do the derivation yourself using Newton’s Laws and the Universal Gas Equation if you make the assumption that the flow of heat from the zones of compression to the zones of rarefaction in the sound wave is too slow to make any difference.
Any meteor you are likely to have seen would have been quite tiny and very high up. I wouldn’t have expected that the sonic boom would have been audible from the ground.
Having dealt with flow in pipes, here are some things you may find of interest:
1> Fluid flow velocity in a pipe will never exceed the speed of sound unless you have a converging diverging nozzle like in jet engines.
2> The pressure wave in a tube travels at the speed of sound. The flow lags this sometimes. What i mean by the pressure wave is that if you have a pipe of length L, and you changed the pressure at one end, the other end comes to “know” of this change at the speed of sound.
It does, a lot. Does this still apply when the pressure change is going from zero to non-zero? In other words, is the leading edge of the pressure wave also the leading edge of the air itself, and traveling at 340.9 m/s? That would mean that a wall of air is colliding with my object, which is already rushing towards it at 300 m/s. Would that be like traveling through stationary air at 640.9 m/s? The big question is, how much would this slow it down? I’m not looking for a number here (too many variables), just a sense. The object itself is pretty sleek and sturdy. It is important to the scene that the object should still be moving pretty fast after the air is introduced.
I think the drag would be proportional to the density of the air. If air is being introduced slowly, the object will initially encounter low density and so be slowed only very little. If the air is introduced suddenly, there will be a “wall” of air traveling roughly at sound speed (I think). So your relative velocity is increased compared to traveling through still air, and this also increases your drag. High-speed drag is proportional to (relative) velocity squared, so the increase will be significant.