Sonic Fluid Flow 2

[venividivici]

Why is sonic velocity the maximum velocity a fluid will flow under typical conditions (fluid flowing from higher pressure to lower pressure). I know that flow becomes choked at Mach=1, but what physically causes this to be the case?

 

[BigInch]

Blowdown

http://www.eng-tips.com/viewthread.cfm?qid=385114

 

[BigInch]

My unscientific opinion is that something similar probably happens to liquids. As we certainly can see sound and pressure waves transmitted though liquids, they must be compressible. I would presume that it happens, but at a far reduced scale. At least it would happen if we could get the liquid moving that fast. Practically in pipe flow I don't think it happens, certainly not often, but I suppose somebody can do it if they have enough power available.

Practically speaking maximum liquid flow through an orifice, or valve, becomes limited when the downstream pressure equals the liquid's vapour pressure. Any extra space around the vena contracta that would normally fill with more liquid becomes instead filled with vaporizing fluid, effectively limiting the flow from increasing any further. As long as downstream pressure is not increased, increasing the upstream pressure would not produce more flow.

 

[zdas04]

I discussed this in faq378-1864 too.

Since the friction factor for liquid is 4 times the friction factor for gases, I've always thought that the shear magnitude of the dP due to friction becomes limiting long before the shock waves can stabilize.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[bimr]

The continuity equation applies to steady flow processes, not to a condition where one is decreasing the downstream pressure. If the fluid is in a steady state, this means mass isn’t accumulating or diminishing. In other words, you’re not doing something like adding a water to a jar. In a steady state, the rate of mass flow must be the same everywhere.

It is a fact that when a gas or vapor is allowed to flow through a conduit or restriction from some fixed upstream pressure to a lower downstream pressure, the mass flow rate increases with decreasing downstream pressure.

Regarding the horse, one can observe that other posters have passed away since you started posting on this same topic in other posts. Perhaps one should take their own advice.

 

[e43u8]

Agreed with bmir; in fact where a compressible subsonic flow is expanding across a nozzle or orifice at constant upstream condition if downstream pressure is decreased the steady state condition being changed and there would be a new condition in which the mass flow rate increases due to fluid velocity increase. Obviously, there is a limiting value called critical flow pressure below which there would be no increament in mass flow rate upon to further decrease in downstream pressure...

 

[BigInch]

Did you read the thread, or only the last entry?

 

[e43u8]

First to last...!

The thread had already been deviated from what OP raised...

 

[BigInch]

Don't understand why subsonic flow is being revisited. I thought the subject turned to limiting conditions, which we seem to be sure are at sonic flow. Changing densities would also change the sonic velocity, which would also change the flow rate at sonic conditions, although the conditions changed, they would still be sonic.

 

[Latexman]

A fair portion of compressible flow threads go off into the weeds!

Good luck,
Latexman

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

 

[e43u8]

In sonic flow across a nozzle or orifice with constant upstream condition, the density change due to a decrease in downstream pressure wouldn't change the sonic velocity; because the downstream pressure is equal to or lower than critical flow pressure and regardless the value of the downstream pressure, a constant mass flow rate will be adjusted by constant upstream pressure and corresponding critical flow pressure...of course if second choked condition being created at downstream it will affect the mass flow rate through the upstream nozzle or orifice...

 

[zdas04]

The weeds are fine, I often have fun in the weeds. I rarely have much fun in Cloud Cuckoo Land. Are we going to start talking about sonic flow into a diverging nozzle (velocity increases) next?

My trip to the weeds was just to point out that velocity was constant in choked flow (by definition), but mass flow rate is only constant as long as upstream pressure is constant and we should stop using mass flow rate in the definition of choked flow. The number of qualifiers that are getting thrown around now is staggering my mind.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[zdas04]

The equation for sonic velocity is

v=(k*R_gas*T)^0.5

(k is the ratio of specific heats, T is in absolute units, and R_gas = R_universal/MW = R_air/SG)

Where is pressure in that calculation? If the flow is isothermal (which is very common both for infinite source problems and for depressurization problems) then the speed of sound is constant.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

I'm happy to believe NASA.

https://www.grc.nasa.gov/

http://WWW/k-12/airplane/mflchk.html

 

[zdas04]

The equation in the red box is a well known compressible flow representation of mass flow rate as a function of Mach number. Nothing in the discussion thus far has treated the flow as compressible, everyone is saying that mass flow rate is ρVA (eq 1 in the NASA file) like it is in incompressible flow.

Equation 2 is the one that I gave you for sonic velocity. Velocity is not a function of pressure or density, just temperature and gas composition.

There is simply nothing in the NASA file that contradicts the statement that in choked flow velocity is constant, but mass flow rate is a function of upstream density.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[BigInch]

I'm not disagreeing with you or NASA.

 

[BigInch]

However, just because density doesn't appear in that equation doesn't mean that sonic velocity does not have a relationship to density, which it has by virtue of gas density's dependency on temperature.

 

[zdas04]

Absolutely. A temperature change, changes density. I didn't say it doesn't. I said that the magnitude of sonic velocity is not dependent on pressure while mass flow is dependent on upstream pressure.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[Latexman]

Velocity is THE fundamental limit for sonic flow. IMO, understanding can be improved by focusing on the fundamentals. However, mass flow rate can be used as a surrogate, if one is careful and understands the additional relationships (density). It's easy to see why mass flow rate is more desirable. The velocity at the choke is a local issue, while all the upstream and downstream equipment must deal with the mass flow rate.

I wonder if this debate led to the derivation of mass velocity back in the day?

Good luck,
Latexman

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

 

[katmar]

I'm surprised this thread hasn't brought Sailoday28 out of the woodwork.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[Latexman]

Hmmm. Sailoday's last log in was on Friday, November 22, 2013! That's 18 months. I hope they are okay.

Good luck,
Latexman

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