speed of a pressure fluctuation in a flowing fluid

[skuntz]

This is related to a real world design issue. If you have a process where the pressure of a compressible fluid is being measured downstream and a sudden change in pressure occurs (e.g. step change), how do you determine the time of propagation between the the point of change and the point of measurement. I have heard replies from two camps: (1) It is the distance divided by the fluid velocity or (2) it is the distance divided by the speed of sound in the fluid. The rationale behind the latter opinion is that a sudden chagne in pressure is the same as sound propagating through a medium.

What is you opinion?

 

[Latexman]

Distance divided by the speed of sound in the fluid.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[bimr]

There is no reason to offer opinions on this matter when facts are readily available.

Distance divided by the speed of sound in the fluid is the better answer, but is not complete. The shape of the container also plays a part.

An important property of pressure is that it is transmitted through the fluid. When an inflated bicycle tube is pressed at one point, for example, the pressure increases at every other point in the tube. Measurements show that the increase is the same at every point and equal to the applied pressure. For example, if an extra pressure of 5 psi were suddenly applied at the tube valve, the pressure would increase at every point of the tube by exactly this amount. This property of transmitting pressure undiminished is a well established experimental fact, and it is a property possessed by all fluids.

The transmission does not occur instantaneously, but at a rate that depends on the speed of sound in the medium and the shape of the container. The speed of sound is important because it measures the rate at which pressure disturbances propagate (sound is just a pressure disturbance travelling through a medium). The shape of the container is important because pressure waves refract and reflect of the walls of the container and this increases the distance and time the pressure waves need to travel. This phenomenon should be familiar to anyone who has experienced the imperfect acoustics of a poorly designed concert hall.

https://www.princeton.edu/~asmits/Bicycle_web/pressure.html

The velocity of a moving fluid in a pipe is approximately 3-10 ft/sec, while the speed of sound is 1,125 ft/s. When you press the hydraulic brake on your vehicle, is there a time lag before the brakes are applied? On the contrary, if the pressure wave traveled at the speed of a moving fluid, there would be a time lag.

 

[btrueblood]

An exception to the above excellent descriptions would be in desribing the head pressure in a wave disturbance moving in a flowing, open channel. there, the wave speed can/will depend on [ fluid depth x gravitational acceleration] ^0.5 , and also depends on whether the flow is super- or subcritical.

 

[77JQX]

The speed of pressure waves in pressurized liquid pipes is called "celerity" in the study of water hammer. It depends on the fluid properties and the rigidity of the pipe walls. The speed of the wave is greater in rigid pipelines, approaching the speed of sound in the fluid, but is decreased by any elastic behavior of the pipe material. Googling "water hammer" should get you plenty of equations to calculate the speed based on the fluid/pipe combination.