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# Compressible Fluid Flow

fluid mechanics compressible flow line losses dp gas phase derivation

5 replies to this topic
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### #1 emma14778

emma14778

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Posted 29 August 2017 - 10:27 PM

I have been trying to figure out how to calculate compressible fluid flow. I have been doing some research and have worked through a derivation for isothermal compressible flow. I keep finding contradicting equations, ones which have gravity included and ones which do not.

I have attached two pictures. One is an isothermal equation from crane TP-10 which includes gravity and the other is from an article by Robert Kern which does not include gravity.

I can follow the derivation in the article up until the point where they simply change units, at this point the gravity term disappears with no mention of it. I have seen this in several different references so I doubt it is just a typo. Can anyone explain why we can neglect the gravity term?

### #2 IGC

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Posted 30 August 2017 - 03:19 AM

Assumption number 7 in the crane paper - the pipe line is straight and horizontal.

www.cchem.berkeley.edu/cbe150a/mom/CompressableFlow.ppt

That ppt has an example of isothermal flow + an energy balance to show why it is neglected.

### #3 breizh

breizh

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Posted 30 August 2017 - 08:03 AM

Hi ,

You may find pointers in this paper.

Breizh

### #4 Bayo Alabi

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Posted 31 August 2017 - 07:19 AM

Can anyone explain why we can neglect the gravity term?

nmoverley,

For all practical purposes, gravity term or potential-energy term is not considered should the density of the gas due to high pressure or high molecular weight be greater than 5 lb/ft3 (80 k/m3) with a difference in elevation of about 50 ft (15 m)

Bayo

### #5 breizh

breizh

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Posted 01 September 2017 - 07:11 AM

Hi ,

let you consider this resource too.

Breizh

### #6 Bayo Alabi

Bayo Alabi

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Posted 01 September 2017 - 09:54 AM

I have been trying to figure out how to calculate compressible fluid flow. I have been doing some research and have worked through a derivation for isothermal compressible flow. I keep finding contradicting equations, ones which have gravity included and ones which do not.

I have attached two pictures. One is an isothermal equation from crane TP-10 which includes gravity and the other is from an article by Robert Kern which does not include gravity.

I can follow the derivation in the article up until the point where they simply change units, at this point the gravity term disappears with no mention of it. I have seen this in several different references so I doubt it is just a typo. Can anyone explain why we can neglect the gravity term?

nmoverley,

I made mistake in my last post. The densities of most common gases and vapours are sufficiently low that differences in potential energy for normal piping configurations and flow conditions are negligible with respect to kinetic-energy changes and friction losses. That's why potential energy changes usually need not be included in the evaluation. However, if your gas density is greater than 80 kg/m3 with a difference in elevation greater than about 15 m, then you should consider potential-energy term.

Bayo