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# Choked Flow in valve2

## Choked Flow in valve

(OP)
Hi,

I would like to know if choked flow can occur in a valve even if the velocity of air passing through the valve has not reached Mach 1.

Also how will I determine is the flow is choked or not, given I know the upstream and downstream pressures.

Thank you

### RE: Choked Flow in valve

If downstream pressure is less than

P(crit)=P(upstream)*(2/(k+1))^(k/(k-1)

Then the flow is critical and velocity is 1.0 M.  For air this works out to 0.528 times upstream pressure (in absolute units).  For typical natural gas (i.e., k=1.28) it is 0.549 times upstream pressure.

David

### RE: Choked Flow in valve

(OP)
Thank you for your replies. I have air coming in at 200 psi and the outlet pressure is 100 psi. The velocity through the valve is not sonic. Will the valve choke? I do realise that P* is 0.528 and Po/Pi = 0.5. Kindly clarify

### RE: Choked Flow in valve

Nalhasimba,
The correlation reported by zdas04 is absolutely right and gives a precise value for the choked flow. I'd just add that "k" is the ratio of the specific heats

k = cp / cv

cp= specific heat capacity for the gas in a constant pressure process  [kJ/(kg K)]

cv =specific heat capacity for the gas in a constant volume process [kJ/(kg K)]

k (very) slightly varies with temperature.

### RE: Choked Flow in valve

If the air is at 200 psig (NEVER say "200 psi" on eng-tips.com, it means nothing and makes it harder for people to help you) and you are at sea level then P(up) = 214.7 psia and P(crit)=113.36 psia=98.66 psig.  As long as the exhaust pressure is less than 98.666 psig then you will have critical flow and velocity will be 1.0 M.

Now if the values you gave were psia then P(crit)=105.6 psia=90.9 psig so with 100 psia downstream you are choked and velocity =1.0M

David

### RE: Choked Flow in valve

Nalhasimba,

When approaching chocked flow problems and related topics (i.e. flow coefficient Cv), always use absolute values for pressures.

### RE: Choked Flow in valve

Being choked is neither bad or unusual for a valve.  If the ratio of (absolute) pressures :inlet/outlet is greater than ~2, then the flow is choked.

Choked does not mean that the flow stops.
Choked does not mean that you can't get any additional flow through the valve.  Just open the valve more and you'll have more flow.
It really only means that the actual capacity is less than that predicted by the noncritical Cv equation.  Once the deviation of the measured flow less than the predicted flow exceeds 2% the flow is said to have choked.
Another thing that happens is if the flow is choked and tnothing else changes, it is possible to lower the downstream pressure additionally wouthout affecting the flowrate.
Once the flow is choked: the math changes and you use a different equation.  Any manufacturer's sizing software is going to address this and automatically shift to the compressible flow routine. The compressible flow routine has 15 variables.  It is not fun.   If you are sizing valves by pencil, paper, and calculator you have too much free time.

### RE: Choked Flow in valve

(OP)
Thank you everyone for your response. I got a air valve sized up by a sales guy for the following conditions.

114.7 psia upsteam
14.7 psia downstream

The Mach number through the sized up valve is 0.85.

Pressure ratio: 114.7/14.7 = 7.8

Choked flow occurs when mach no is 1. But in this case mach number through the valve is less that 1. Can choked flow still occur @ M=0.85? I get the math and know what happens during choked flow.

In this case things look contradicting and I am a little confused.

Thank you

### RE: Choked Flow in valve

How have you computed the Mach number?

### RE: Choked Flow in valve

It's definitely a choked flow application.

You have (or should have ) the Cv of the valve and so you can calculate your gas flow rate.
I use Kv instead of Cv as I am more familiar with (Kv = 0.853 *Cv)

Q = 480.4 * Kv * SQRT[(deltaP*Pd)/(T*rhorel)]

Where:

Q = gas flow rate, normal cubic meter per hour
Pd = outlet gas absolute pressure (bara)
deltaP = pressure difference (bar)
T = gas absolute temperature (K)
rhorel = gas density compared to air (in this case = 1)

At this point you can calculate your gas speed

V = 1.222 * (Q*T)/(Pd*D^2)

where:

V = gas speed (m/s)
Q = gas flow rate, normal cubic meter per hour
T = gas absolute temperature (K)
Pd = outlet gas absolute pressure (bara)
D = internal valve diameter (mm)

Then you can calculate M = V/u (with u speed of sound in the medium)

### RE: Choked Flow in valve

With a discharge to atmosphere, your salesman (or his program) is simply wrong.  Sorry, but the arithmetic works out to Mach 1.0 and a program that disagrees with that is wrong.

David

### RE: Choked Flow in valve

(OP)
Correct me if I am wrong.

Pdownstream = 14.7 psia
Critical pressure ratio for air = 0.528

Pupstream = 14.7 / 0.528 = 27.8 psia

Hence the flow must be choked if the upstream is at 27.8 psia and the outlet is at 14.7 psia.

However increasing upstream pressure will increase the mass flow rate as the density increases and hence mass flow increases. Based on this if I increase the upstream pressure to 100 psia I should be able to get higher mass flow.

I do appreciate the time you are taking to clarify my question.

In regards to mach number of 0.85, i didn't calculate it. I was given to me by the sales guy.

### RE: Choked Flow in valve

It is not a good idea to work this problem backwards, you end up with odd velocities.  Start with the upstream pressure (114.7 psia) and apply the critical flow equation and the maximum downstream pressure that will give you sonic flow is 60.56 psia.  Any pressure less than that number will give you exactly the same mass flow rate, velocity, and volume flow rate.

In your example, 27.8 psia upstream of an exhaust to atmosphere would give you choked flow, but since the upstream pressure is so much lower, the mass flow rate, velocity, and volume flow rate would be a fraction of their values at 114.7 psia upstream.

With regard to your salesman telling you that the velocity was less than Mach 1.0 there is a time that that number would be right--if the valve configuration forced a pressure drop between the valve seat ant the actual exhaust then you would never see pressure below critical until the exit plane of the exhaust pipe.  This could happen if there is a lengthy tail pipe or a tortuous path through the valve.  In this case, the pressure immediately downstream of the valve seat could be slightly higher than 60.56 psia, and the remainder of the pressure drop is taken incrementally through the ports and down the tail pipe.  If that happened then you could be a a fraction of Mach 1.0, but I've never seen a valve with that much pressure drop after the seat.

### RE: Choked Flow in valve

nalasimbha,

Please take a look to the link below: you'll find the undeniable mathematical evidence that for chocked flow (assuming air as an ideal gas) the Mach number must be equal to 1.

http://wins.engr.wisc.edu/teaching/mpfBook/node18.html

There must be something wrong with the program that calculated M=0.85

### RE: Choked Flow in valve

I cannot believe that anyone here would doubt the information provided by a salesperson or her software.

One of those manufacturers also claims that the velocity in the vena contracta is not important for valve wear.

### RE: Choked Flow in valve

In the case of CCI Self valves, considering  the stacked discs and the engineered change of area as the fluid passes thru the stacks, one can have Pi/Po = 7.5 :1 and not have acoustically choked flow . The flow is frictionally choked instead. ( Xt=1.0)

The above postings that correlate (acoustically) choked flow with a critical pressure ratio and ratio of specific heats are at best describing the choking that occurs across a simple ball valve. Any other valve with complex internal geomety will experience "oblique shock waves" at a pressure ratio less than the acoustic limit, and such typical valevs ould have their choked or critical flow computed using the ISA method , which includes the factors Cv, Xt, ratio of specific heats, etc.

### RE: Choked Flow in valve

davefitz,

Anyhow I consider that our attention should be focused on what "choked" is referred to.
The adjective "choked" (IMO) should be more properly referred to a particular fluid velocity than to flow (mass) as this condition defines an upper limit for the velocity and not for flow (mass). In choked conditions, the mass flow rate could be anyway be increased as upstream absolute pressure is increased (density increases). So if we are talking about choked condition, this should imply M=1.

### RE: Choked Flow in valve

(OP)
Thank you everyone for your inputs and clarifying my question.

### RE: Choked Flow in valve

I'm not sure where this error in people's thinking is coming from, but the speed of sound is NOT a physical constant.  It is a function of fluid density.  So if you increase upstream pressure, the speed of sound increases. If you decrease upstream pressure, the speed of sound decreases.  Consequently, the REASON that mass flow rate will increase with increasing velocity is BECAUSE the velocity increased.  Several posts above have tried to make a distinction between velocity (as a constant) and mass flow rate (as an unrelated variable) and that distinction is not correct.

The definition of "Choked flow" above is correct.  Our interpretation of it is often flawed.  The "upstream" and "downstream" pressures refer to adjacent points across a single restriction.  A valve with 5 pressure drops that has a large enough pressure drop across the entire valve to be choked could easily never have a single pair of adjacent points that satisfy the conditions for choked flow so you never get to Mach 1.0.

The OP said he had a "valve" and we all assumed it was a simple globe valve with a single restriction.  If that assumption was correct then the discussion above is on point.  If that assumption was not correct then maybe the OP is in a better position now to understand what his vendor is telling him.

David

### RE: Choked Flow in valve

>>the speed of sound is NOT a physical constant.  It is a function of fluid density. <<

My Marks Handbook shows the calculation for the Spped of sound in air as V=49.1 * Sqrt T
V is in fps, T is in degrees R

No density parameter there....

Aircraft experience sonic flight more easily at higher altitudes because the air is cooler, thus Mach1 is slower.  Certainly intertial effects diminish due to less dense air at higher altitudes to let a plane go faster with less thrust.

ione is right.  Increase the upstream pressure and you'll increase the mass flow rate thru a fixed restriction.  If the flow is choked it will be independent of the downstream pressure

### RE: Choked Flow in valve

speed of sound is related to density,
c^2 = dp / drho
where c is speed of sound, p pressure and rho density

a decent software for control valves design / rating should evaluate the speed of sound at outlet conditions, I use this (free) tool

http://www.prode.com/en/valves.htm

however most manufacturers provide this kind of software with the FL, XT etc. coefficients required by ISA/ISO codes.

### RE: Choked Flow in valve

speed of sound is related to density,
c^2 = dp / drho
where c is speed of sound, p pressure and rho density

a decent software for control valves design / rating should evaluate the speed of sound at outlet conditions, I use this (free) tool

http://www.prode.com/en/valves.htm

however most manufacturers provide this kind of software with the FL, XT etc. coefficients required by ISA/ISO codes.

### RE: Choked Flow in valve

JimCasey,
Careful with that simplification.  It comes from

c^2=k*g*R(gas)*T

Starting with air and assuming that "k" is not a function of pressure and adding some unit conversions gets you to the constant you mentioned.  In that single case your equation works fine.

The equation does come from dP/drho at constant entropy like PaoloPemi said, but if you note that P/rho=RT then you see where the pressure term falls out.

I've just spent a half hour in MathCad tweaking numbers and I keep reaching the same conclusion that several of you have come to--changing pressure at constant temperature does not change sonic velocity, but it does change mass flow rate.  I'm not sure I know how to get my mind around this, but I'm working on it. I do know that I was wrong and several of you were right.

David

### RE: Choked Flow in valve

David,

We have always to speak about "speed of sound in a medium" and not generically about "speed of sound". It is the velocity the wave (sound) travels in a medium and so it varies with the medium properties. But in the assumptions of the posts above (those which led to M = 1 in choked conditions), air is always considered as an ideal gas. For an ideal gas and at a constant temperature, pressure has no effect on the speed of sound, because pressure and density have counterbalancing effects.

### RE: Choked Flow in valve

when sizing/rating a control valve one has to figure out values for Xt, Fl and other parameters mentioned in standards, in general it's better to leave this responsability to manufacturers...
At low pressures (as those mentioned in previous posts) the influence of pressure is limited, using Prode Properties (but other tools should give similar values) I calculated speed of sound in air with PR and SRK models

Air Mol. comp.
N2 0.78082
O2 0.2095
Ar 0.0093
Co2 0.00038

Press. 14.7 Psi.a
T (F)    PR m/s    SRK m/s
0    320.41    320.55
20    327.32     327.46
40    334.08    334.21
60    340.69    340.82
80    347.17    347.29
100    353.52    353.64
120    359.75    359.86
140    365.86    365.96
160    371.86    371.96
180    377.75    377.84

Press. 114.7 Psi.a
T (F)    PR m/s    SRK m/s
0    320.24    321.34
20    327.36    328.41
40    334.30    335.30
60    341.07    342.02
80    347.68    348.59
100    354.15    355.02
120    360.48    361.31
140    366.68    367.48
160    372.75    373.52
180    378.71    379.45

in this range of pressures and temperatures the assumption of ideal gas should not give too bad results.

### RE: Choked Flow in valve

To better explain:

For the flow rate:

Q = rho*v*A

Where:
Q = flow rate
rho = fluid density
v = fluid velocity
A = cross sectional area

As you increase upstream absolute pressure the fluid density increases accordingly thus leading to mass flow rate increase, and this happens independently from the downstream absolute pressure.

At the same time, considering air as an ideal gas and for isentropic process

p/(rho^k)  is constant during an isentropic process

(dp/drho)isentropic = k*(p/rho) = k*R*T

Where:

k = ratio of specific heats
p = pressure
R = gas constant
T = absolute gas temperature

From the speed of sound c definition

c^2 = dp/drho => c = SQRT (k*R*T)

So at constant temperature c is constant (for a specific medium)

### RE: Choked Flow in valve

Its been over 25 yrs since I took the compressible fluid mech course, but the speed of sound is related to the mean molecular transverse velocity, which  is proportional to the absolute temperature to some power.  Molecular weight is also involved in the relationship, which makes it appear that density is involved, but the density is not the driver- its the speed of the speed of the molecules as they bounce around.

### RE: Choked Flow in valve

A mistake in my previous post.
The molar mass M (kg/mol) of the medium enters the formula for the speed of sound (ideal gas and isentropic process):

c = SQRT (k*R*T/M)

Anyhow this doesn't change how things are: for ideal gas and isentropic process the sound of speed is constant at constant temperature (independently from the pressure).

### RE: Choked Flow in valve

Back to the question,
The Salesman's software probably has the inside diameter of the pipe imbedded as a table.  It is reporting the velocity downstream in either the body or in the pipe.  The velocity thru the vena contracta or even thru the trim annulus will be sonic.  With 0.85M downstream, it's likely to be quite noisy, too.

### RE: Choked Flow in valve

a important factor to consider is the noise due to flashing / cavitation / critical flow, we had a control valve that under certain conditions did produce a lot of noise, the plug had to be replaced at regular intervals and at last we decided to replace the valve. Unfortunately the manufacturer's software wasn't able to predict the problem.

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