Does orifice diameter affect critical pressure when testing for choked flow?
Does orifice diameter affect critical pressure when testing for choked flow?
(OP)
Does orifice diameter affect critical pressure through a converging nozzle, or is it entirely dependent on the ratio of inlet and outlet pressure? (assume Isentropic flow of air). References from other forum posts listed at the bottom.
I've seen many references for testing for choked flow using the following equation that depends only on pressure, not orifice diameter. Assuming dry air (k = 1.4), this works out to P/Po < .5283 for sonic flow (M=1) to occur.

Does orifice diameter have any effect on this? For example, if I enlarged the orifice to 99% on the inlet pipe diameter, wouldn't sonic flow cease to occur?
The formula for mass flow seems to reinforce that orifice area only scales the mass flow, with no effect on when max flow peaks (i.e. at sonic speeds, M = 1).

Am I thinking of this correctly? What gives?
Posts from other forums regarding choked flow:
[FAQ798-1196: Mass flow rate of a gas through an orifice during choked conditions]
[FAQ1203-1293: A Simple Numerical Method for Gas/Vapor Flow in a Safety Valve]
Other guides on sonic flow I have studied but had a hard time digesting.
[http://highered.mcgraw-hill.com/sites/dl/free/0072...]
[http://www.engr.ipfw.edu/~renie/ME301%20Page/ch16....]
Thanks in advance for straightening me out!
I've seen many references for testing for choked flow using the following equation that depends only on pressure, not orifice diameter. Assuming dry air (k = 1.4), this works out to P/Po < .5283 for sonic flow (M=1) to occur.

Does orifice diameter have any effect on this? For example, if I enlarged the orifice to 99% on the inlet pipe diameter, wouldn't sonic flow cease to occur?
The formula for mass flow seems to reinforce that orifice area only scales the mass flow, with no effect on when max flow peaks (i.e. at sonic speeds, M = 1).

Am I thinking of this correctly? What gives?
Posts from other forums regarding choked flow:
[FAQ798-1196: Mass flow rate of a gas through an orifice during choked conditions]
[FAQ1203-1293: A Simple Numerical Method for Gas/Vapor Flow in a Safety Valve]
Other guides on sonic flow I have studied but had a hard time digesting.
[http://highered.mcgraw-hill.com/sites/dl/free/0072...]
[http://www.engr.ipfw.edu/~renie/ME301%20Page/ch16....]
Thanks in advance for straightening me out!





RE: Does orifice diameter affect critical pressure when testing for choked flow?
The NASA equation understates the effect of the transition from pipe flow to unconstrained flow and overstates flow, but the implication that sonic velocity is not a function of either hole size or how far the upstream pressure is above choked flow is correct.
David Simpson, PE
MuleShoe Engineering
"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"
RE: Does orifice diameter affect critical pressure when testing for choked flow?
RE: Does orifice diameter affect critical pressure when testing for choked flow?
David Simpson, PE
MuleShoe Engineering
"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Sorry. But Choked flow occurs when the mass flow will not increase as back pressure is lowered. AND upstream conditions are fixed.
Regards
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Sorry, but you are quite wrong. Choked flow occurs when VELOCITY will not increase when either downstream pressure is lowered or upstream pressure is raised. Fixed upstream pressure is not a requirement.
Think about it. You have a system at 10,000 psig blowing down to atmosphere. The velocity will stay at Mach 1.0 until upstream pressure gets to some number around 15 psig, and then further decreases in upstream pressure will reduce velocity.
Since mass flow rate is ρ*V*A, as pressure drops (with constant V and A), the mass flow rate will drop.
The only requirement for choked flow is that downstream pressure is less than Pchoked
David Simpson, PE
MuleShoe Engineering
"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"
RE: Does orifice diameter affect critical pressure when testing for choked flow?
RE: Does orifice diameter affect critical pressure when testing for choked flow?
David Simpson, PE
MuleShoe Engineering
"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Independent events are seldomly independent.
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Consider a perfect gas with constant specific heats undergoing an isentropic process.
Energy equation ao^2= a^2 + (gamma-1)/2 *u^2
where a= sound speed u= local velocity and subscript o stagnations coditions
For isentropic process (rho/rhoo)= (a/ao)^(2/(gamma-1))
Substitute G/rho for u in the energy equation where G is the mass flus
Differentiate the energy equation with respect to G
and you will get a/ao=2/(gamma-1) after setting derivate wrt G =0
Substitute a/ao into energy equation yielding Mach=1.
Pressure relation could have been substituted for a. See next sentence.
p/po=(a/ao)^((2gamma/(gamma-1)) ie pv^gamma =constant Substitute for a/ao will yield critical pressure ratio
In other words for steady flow M=1 when mass flux is a max.
I did the above in haste and there can be an algebraic error, however I know from my basic days in engineering that choked flow occurs when lowering back pressure will not increase the mass flow
Regards
RE: Does orifice diameter affect critical pressure when testing for choked flow?
Independent events are seldomly independent.
RE: Does orifice diameter affect critical pressure when testing for choked flow?
I agree that the parameter which is choked (limited, constrained) is velocity, I agree as well that you can increase mass flow, but not acting on downstream pressure.
At choked condition the mass flow rate Q is given by:
Q = C*A *SQRT[(kM/ZRT)*(2/(k+1))^((k+1)/(k-1))]
Q = mass flow rate
C = discharge coefficient
A = orifice hole area
k = gas cp/cv = ratio of specific heats
ρ = real gas density, at upstream P and T
P = absolute upstream pressurE
M = gas molecular weight
R = Universal Gas Law constant
T = gas temperature
Z = the gas compressibility factor at P and T
So Q is independent from downstream pressure.
What I consider flawed in David’s line of reasoning is:
“Since mass flow rate is ρ*V*A, as pressure drops (with constant V and A), the mass flow rate will drop”
“A” is not constant at vena contracta if you vary downstream pressure. So the velocity is limited (choked) at M=1, but you can in any case increase Q increasing the upstream pressure.
RE: Does orifice diameter affect critical pressure when testing for choked flow?
David Simpson, PE
MuleShoe Engineering
"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"
RE: Does orifice diameter affect critical pressure when testing for choked flow?
I thought, but I might be wrong, in your post dated back 26 Sep 13 18:55 you meant that A was the area at vena contracta. Now if you change the downstream pressure (change with time) A is not constant anymore with time, but it will rather increase as density ρ, at downstream conditions, will decrease.
So I firmly agree with you that "The only requirement for choked flow is that downstream pressure is less than Pchoked", but when choked flow condition is satisfied, any further decrease in downstream pressure won't produce any increase of mass flow (and I think this what Sailoday28 was saying, or at least this is how I have interpreted his/her post). When choked flow condition is satisfied the only way to increase mass flow is to act on upstream condition (i.e. increase upstream pressure).
RE: Does orifice diameter affect critical pressure when testing for choked flow?
A can vary. In my formulation, I use G, which is the mass flux or W/A.
Regards