Negative Pressure Wave generation due to pipeline leak

[leakdetector123]

TL;DR Summary

when leak happens in the pipeline a negative pressure wave is generated can anyone explain how it is generated and why in many research paper it is mentioned that this wave travels at sonic speed( speed of sound )?

consider a simple straight gas pipeline

please refer below attached file for further details

 

[Baluncore]

The negative pressure transient is generated by the sudden increase in flow, out of the transmission line.
It is the negative equivalent to water hammer, that is transmitted back up the line when a valve is suddenly closed.
The pressure wave propagates up the line at the speed of sound in the fluid.

 

[leakdetector123]

The negative pressure transient is generated by the sudden increase in flow, out of the transmission line.
It is the negative equivalent to water hammer, that is transmitted back up the line when a valve is suddenly closed.
The pressure wave propagates up the line at the speed of sound in the fluid.

is there any specific reason or explanation as for why pressure wave propagates at the speed of sound in fluid

 

[Baluncore]

is there any specific reason or explanation as for why pressure wave propagates at the speed of sound in fluid

The speed of sound is a function of temperature, because temperature determines the average velocity of the molecules in the fluid.

 

[leakdetector123]

The negative pressure transient is generated by the sudden increase in flow, out of the transmission line.
It is the negative equivalent to water hammer, that is transmitted back up the line when a valve is suddenly closed.
The pressure wave propagates up the line at the speed of sound in the fluid.

can you explain how this pressure transient travels
what i am thinking is that when leak happens a low pressure region is generated near the leak and the molecules in the high pressure region in pipeline travels to the low pressure region hence creates the low pressure region in the place where previously high pressure existed and so on this low pressure region travels across the pipeline
is that correct?

 

[Baluncore]

is that correct?

Yes. It is a loss of support.

The average kinetic energy of the molecules in the fluid, is proportional to temperature. The average velocity of the molecules in the fluid, is therefore proportional to the square root, of the fluid temperature.

The pressure waves, that propagate away from the burst of a pipeline, will also be influenced by the velocity of the fluid flow in the pipeline, immediately prior to the burst. That will introduce a Doppler effect, that will differentially scale the time axis for the transients, at the ends of the line. That may influence the cross-correlation process.

The attenuation of the transients, will also be dependent on travel time, through the fluid. That will change the amplitude scale of the transients. Cross-correlation will ignore the differential attenuation. That will result in the loss of any range information, that might have been present in the transient amplitudes.

 

[Chestermiller]

If you do a differential force balance on the gas within the section of pipe between x and x +dx and assume that all gas expansion and compression occurs adiabatically, you end up with a wave equation for the pressure as a function of time and position. The characteristic speed of the wave propagation in this equation is equal to the speed of sound.

 

[leakdetector123]

If you do a differential force balance on the gas within the section of pipe between x and x +dx and assume that all gas expansion and compression occurs adiabatically, you end up with a wave equation for the pressure as a function of time and position. The characteristic speed of the wave propagation in this equation is equal to the speed of sound.

i understand when leak happens the gas expands but how does the gas compresses

 

[Baluncore]

The pipeline contains compressed gas.