The definition of choked flow is when a reduction in downstream pressure does not result in an increase in flow through an orifice. In the case of a tiny hole in a pipe if flow becomes sonic it will also be choked.

My question is... if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?

zdas04 (Mechanical) 23 Apr 08 7:17 Yes, "choked flow" implies that the exhaust stream is initially moving at Mach 1.0.  That velocity never lasts very long because of fluid friction and changing the momentum of surrounding gas molecules immediately begin slowing it down, but the velocity at the exit plane is Mach 1.0.

The harder I work, the luckier I seem  Choked flow may occur with less than  1.0 mach number- if there are sharp angles then there can occur "oblique shock waves" when the average velocity thru the hole is less than the speed of sound.

For example, flow thru some control valves , such as a globe valve, implies sharp angles and changes of direction.  This is described by the "ISA handbook of control valves" as when the Xt is greater than 0.1  . For a streamlined ball valve Xt=0.1, and no oblique shock waves form. For a typical globe valve, Xt=0.8 and oblique shock waves do form and choked flow will occur at a pressure ration less than critical. For a CCI drag valve , Xt=1.0, and no shock waves form and the flow is frictionally choked, not acoustically choked.

In the case of choked flow thru a hole in the pipe, the discharge coeficient is about Cd=0.82, but will vary according to the ratio of the hole diameter to the wall thickness of the pipe. So, based on 100% hoel area, it never reaches sonic velocity , but based on an apparent vena contracta or due to oblique shock waves it becomes choked.

If the process is other than adiabatic, say, isothermal the flow will not choke at Mach=1.

sailoday, can you provide an example of an isothermal flow in conditions described by choked flow (i.e., downstream pressure < upstream pressure * (2/(k+1))^(k/(k-1)))?

Davefitz,  I've found that in the conditions you describe (i.e., standing shock waves downstream of the restricting element) that the pressure at the outlet of the restricting element is higher than the critical pressure from the equation above and the flow is not choked.

My experience says that if you satisfy the equation above, then the velocity will be 1.0 Mach at that exact point.  If something downstream restricts the mass flow rate then pressure will increase at the restrictive element and the conditions for choked flow will no longer be satisfied.

sailoday28 and zdas04, isothermal choke flow may occur in longer pipe lines, that choke at some expansion.

But my understanding was always that Mach=1 in both cases, it is just that sonic velocity for

isothermal flow is different from adiabatic flow.

After reviewing my copy of "The Dynamics and Thermodynamics of Compressible Fluid Flow" by Shapiro, the isothermal flow model falls apart at M = 1/k1/2, where an infinite heat transfer per unit length is needed to maintain a constant temperature.  In reality when a subsonic isothermal flow approaches this limiting Mach Number, all fluid properties change rapidly with distance.  Unless heat is transferred purposely, flow is likely to be more adiabatic than isothermal. Good luck, Latexman

My question is... if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?You clearly have chosen an excellent reference(Shapiro), however, choking can occur at other than M=1.

if you have choked flow does it necessarily mean you will have sonic flow? i.e. can choked flow exist for sub-sonic velocities?

The velocity of sound is thermodynamically defined as a small compression wave moving adiabatically and frictionlessly through the medium.  This is an isentropic process.  If the actual flow process deviates from this, for example the flow is isothermal or there is significant friction or the flow is not adiabatic, it should not be surprising that choked flow can occur at velocities other than sonic.

If a = acoustic velocity (velocity of sound) and a' = the limiting velocity of isothermal flow, then a = a' x k1/2. Good luck,Latexman

In isentropic flow (adiabatic + small friction loss), just as isothermal flow, the mass velocity reaches a maximum when the downstream pressure drops to the point where the velocity becomes sonic at the end of the pipe (e.g., the flow is choked).

But given:c = speed of soundM = molecular weightR = gas constantv = spatial averaged velocityT = constant temperature1 = reference point 12 = reference point 2* = sonic state

Under isothermal conditions, choked flow occurs when:v2  = c = v2* = (R*T/M)^0.5

Under Adiabatic conditions (or locally isentropic), choked flow occurs when:v2 = c = v2* = (k*R*T2/M)^0.5

I have Ron Darby's book and I really don't agree with saying c = v2* = (R*T/M)^0.5 for

isothermal flow.  The speed of sound has a very precise thermodynamic definition:

c = (gc(dP/dρ)S)1/2

One cannot calculate with 100% rigor the speed of sound of a medium in isothermal flow.  This is due to the constant entropy constraint in the definition of the speed of sound.  Isothermal and isentropic conditions are definitely not the same thing.

It's a good book, but being too loose with precise thermodynamic definitions makes this section a bit sloppy in my opinion. Good luck,

I would argue that the mathematics say that isothermal flow chokes at M<1 and the equations are consistent.

However, I would also argue that at the moment that an isothermal flow chokes, an infinite amount of heat is needed to be transferred into the gas in order to maintain the temperature of the gas.  Since this is physically impossible, the temperature must change, and isothermal flow cannot exist in a choked state. I'd say the equations are physically meaningless at that point and so choked isothermal flow cannot happen in reality.  Before you reach the choke point, any real system must always diverge from isothermal conditions.

Exactly how long the isothermal flow equations adequately describe a flow as its velocity builds up depends on the gas, but I'd say that it's pretty conclusive that they do not realistically describe choked flows.

Doh.  How long the isothermal flow equations hold up depend on the state of the gas and the amount of heat that can get into the gas (i.e. surroundings), not just the state of the gas.  

The isothermal equations work really well for a body moving in an infinate reservoir (fighter planes at Mach 3 may heat themselves up, but they don't change the temperature of the atmosphere a measurable amount).  There are really no situations where the equations work when the fluid must reach this speed (instead of the body within the fluid).

Feric (Mechanical) 24 Apr 08 16:31 Hi there:

Here is an online calculator that can help you with compressible flow calclations:http://engware.i-dentity.com/calc5.htm 字串 9

Once you get to the chocked conditions, the downstream flow can become either supersonic or subsonic ...

Your response of"One cannot calculate with 100% rigor the speed of sound of a medium in isothermal flow."Sound speed in isothermal flow is per the definition in your responsec = (gc(dP/dρ)S)1/2  or- with or without isothermal flowc^2=gamma (dp/droh)isothermal

Maybe I'm making too much of a big deal of the definition of sound speed being for isentropic conditions.  What got me started was the equations in Darby's book:

c = (kRT2/M)1/2 for Adiabatic flow 字串 3

and

c = (RT/M)1/2 for Isothermal flow

but

(kRT2/M)1/2 is not = (RT/M)1/2

A different symbol should have been used for the isothermal case or subscripts or something.  It's confusing.  Anyway, whether one uses c2 = (dP/drho)S or k(dP/drho)T they are calculating sound speed for isentropic conditions in both cases.  I don't see how this has meaning to the limiting velocity for isothermal conditions which = c/k1/2 or (dP/drho)T (with no k in the equation). Good luck,Latexman

Thank you Latexman for this clarification. Indeed, Darby's equation for isothermal flow may appear confusing. To me it is simply a typing mistake. Indeed:

Under Adiabatic conditions (or locally isentropic), choked flow occurs when: 字串 1 v2 = c = v2* = (k*R*T2/M)^0.5

Under isothermal conditions, choked flow occurs when:v2 = c/(k^0.5) = v2* = (R*T/M)^0.5

  "We don't believe things because they are true, things are true because we believe them.""Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."  Quote:

... the mass velocity reaches a maximum when the downstream pressure drops to the point where the velocity becomes sonic at the end of the pipe.

The linear velocity (i.e., distance per unit time) reaches a maximum but the mass velocity (i.e., mass per unit time) does not reach a maximum. The mass velocity can be increased by simply increasing the upstream pressure (which increases the upstream gas density). Milton Beychok He should have said "velocity reaches a maximum for a given upstream pressure ...".  Raising the upstream pressure will increase both the linear velocity and the "mass velocity" whatever that is.  We're talking about the speed of sound, and the density of the upstream fluid is a part of that equation.

I don't understand why you said "whatever that is" in your above statement. The speed of sound is a linear velocity (i.e., distance per unit time, such as m/s or ft/s). Mass velocity is mass per unit time such as pounds/s or kilograms/s.

Since the original poster in this thread was interested in the flow from a "tiny hole in a pipe", it might be well to use the equation for choked flow which is very widely used for just that sort of accidental gas release. In SI metric units, when the gas velocity is choked, the equation for the mass flow rate is:

[It is important to note that although the gas velocity reaches a maximum and becomes choked, the mass flow rate is not choked. The mass flow rate can still be increased if the upstream source pressure is increased.]

Q = mass flow rate, kg/sC = discharge coefficient (dimensionless, about 0.72)A = orifice hole area, m2

k = gas cp/cv = ratio of specific heatsρ = real gas density, kg/m3, at upstream P and TP = absolute upstream pressure, PaM = gas molecular weight (dimensionless)R = Universal Gas Law constant, (Pa)(m3 / (kgmol)(°K) 字串 8 T = gas temperature, °KZ = the gas compressibility factor at P and T

Choked flow occurs whenever the ratio of the absolute upstream gas pressure to the absolute downstream gas pressure is equal to or greater than [ ( k + 1 ) / 2 ] k / ( k - 1 ), where k is the specific heat ratio of the gas.

  "Mass velocity" simply does not mean anything.  The quantity you described is actually "mass flow rate".  "Velocity" is a distance over a time in a direction ("speed" is a distance over a time).  Mass per second does not meet the definition.

And, if the upstream pressure increases, then the velocity will increase AND the mass flow rate will increase.  Sonic velocity is dependent on the media in which the sound is traveling--if the media becomes more dense then the speed of sound increases.  In the equations you re-quoted above, the mass flow rate (that I've never seen given the designation "Q" before, but that is a quibble) will increase as the pressure increases--SO WILL THE VELOCITY.  By the way the limiting equation that you included is the same one I posted in this thread three days ago.  

The only thing special about choked flow is that as long as the pressures satisfy the limiting inequality the downstream pressure does not matter.

In the reference i mentionned in post dated 24 Apr 08 11:11 (Darby 2001) the mass velocity is the mass flux: G = m / A = rho*v, with:m: mass flow rateA: cross sectionnal arearho: density

v: spatial averaged velocity "We don't believe things because they are true, things are true because we believe them."

       I agree with you that there is no such thing as mass velocity. As you say you can have "mass flowrate" or velocity but not mass velcity. even the units quoted of kg/s are not "velocity" related.

In the Chemical Engineering field, mass velocity is a term used commonly.  Mass velocity = G = mass flow rate divided by flow area perpendicular to flow.  It is more properly called mass flux, but mass velocity is used by many references. Good luck,Latexman

I don't believe we should get bogged down by semantics. Each science or engineering discipline has its own jargon. As Latexman said, chemical engineers often use the term mass velocity. But whether we call it mass velocity, mass flow rate or mass flux, the equations I gave above speak for themselves in the universal language of mathematics and the references that I gave also speak for themselves. In fact, you will note that when I presented the choked flow equations, I also used the term mass flow rate.

Nor does it matter whether the mass flow rate (mass velocity) is expressed as Q or G or m or whatever, as long one spells out what the symbols are.  What I like about the equations that I gave is that they don't get involved with Mach numbers or the speed of sound, which in my opinion is much simpler

As I said before, the equations that I gave have been used for the last 15-20 years in quantifying accidental releases of gases from piping or vessel holes or similar release sources for the consequence analyses required by law ... not only in the USA but in some other countries as well 

To clear up a simple point, a flow is choked when for given upstream conditions, the mass flux; W/A, will not incrrease when the back pressure is lowered.

Just add the one sentence: "However, the mass flux will increase if the upstream pressure is increased."

What you are saying is incorrect.  If the upstream pressure increases then BOTH the mass flow rate and the velocity increase.  If upstream density decreases then BOTH mass flow rate and velocity decrease.

The only time mass flow rate and velocity are constant is when upstream pressure and temperture are constant and a change in downstream pressure does not take you out of choked flow.

I guess we will just have to agree to disagree. If you look at these "choked flow" equations:

or this equivalent form:

It is obvious from the above equations that the mass flow rate (Q) increases if the upstream pressure (P) is increased ... but the gas velocity is still choked meaning that the linear velocity is still the maximum velocity (i.e., sonic velocity).

That's correct, but let's not forget that the sound speed in gases measured by (k×P÷ρ)1/2 changes slightly in line with the correction by zdas04.

Thank you for input in helping to correct the misconception of choked flow increasing with upstream pressure increases.

The critical pressure ratio, can be easily obtained by fixing upstream conditions and calculating mass flux as back presssure is lowered. The critical pressure ratio is reached when the mass flux no longer increases as back pressure is lowered.--When you increase upstream source pressure after the critical pressure ratio is reached, the source stagnation conditions are changed--as pointed out by zdas04 (Mechanical) 字串 5 MOre simply-for isentropic flow AND fixed upstream condtions, combine the conservation of mass and energy equations-take the derivative of G,(W/A), with respect to back pressure and the choked flow equations and critical pressure will be obtained when dG/dp=0.

I don't disagree with you with regards to infinite Q at critical flow for isothermal conditions. My Shapiro is in storage and I don't remember the proof of infinite Q. Is it it the text or do you remember the derivation?

I don't believe there is a derivation.  The text says something like, "it's obvious from Equation number ?".  That equation is in the form of T/T* and when you do some simple algebra you can see it is indeterminate at c/k1/2.  You have to infer there must be infinite heat transfer per unit length to counter the infinite T/T* in the equation referenced. Good luck, Latexman

There are two formualas given on this thread for the mass flow rate,Q.   The pressure, temperature an density should be at the upstream STAGNATION conditions.

The second formulation includes a term,k,which one MIGHT presume to be the same specific heat ratio specified in the first equation.  Including compressiilty being a constant,  Cp-Cv=ZR and the k should be adjusted accordingly.  Obtaining a Cp or Cv allows computation of k.I would be interested in how either the Cp or Cv is obtained.

Further for choked flow, I would expect a different critical pressure ratio, than that used with the first equation

Consider a horizontal constant ID duct/pipe.momentum equationudu/dx  + vdp/dx    +fu*u/(2D)=0       (1)G=mass flux, rho*ud(lnu)/dx +  dp/dx/(G*G*v)  +f/(2D)=0    (1a)

isothermal flow

d(lnu)/dx   pdp/dx/(G*G*RT)  +f/(2D)=0    (1a)conservation of massPu=constant                                (2)combine (1a) and 2-d(lnp)/dx  + pdp/dx/(G*G*RT)  +f/(2D)=0     (3)

integrate 3-ln(p2/p1)+ (p2*p2-p1*p1/(2G*G*RT)+fL/(2D)=0   (4)

To obtain Gmax, for a given L  differentiate G wrt P2

p2*p2=G*G*RT    but    p2=rho2RT  and G=rho2*u2This will yield u2*u2=RT= a*a/ gamma    where a = sound speed     u/a= M= sqrt(1/gamma)

Substiture p2 into  (4) and get relation of length to choked flow.

Please check for algebraic errors

For isothermal process, pgas.  dh=0anddQ/dx  =udu/dx    substitute into above equations at choked flow  and udu/dx=friction/zero   infinite heat transfeR

Couple of things.  With the confusion that has existed in this thread about terminology, what is "u", "v" (I'm assuming you are using the Fluid Mechanics convention of "u' being velocity in the "x" direction and "v" being velocity in the "y" direction, but I don't want to start analysing your arithmetic withou knowing for sure). 字串 4

Also, I'm looking at a p-h diagram on my wall (you caught me when I was working of options for a CO2 sequestration project) and an isothermal process is anything but constant enthalpy and dh never equals zero (i.e., the constant temperature line on a p-h diagram is never vertical).

is specific volume dh=0 for pv=RT    Try the CO2 and low press high temp and look at const enthalpy lines.  

That is in the liquid region (and looking at the data, the lines are almost vertical, but not quite).  I thought this was primarily a gas discussion and those lines are not even close to vertical compared to the grid (they leave the saturation bubble horizontal and then turn toward vertical, but don't make it).

That is in the liquid region-Generally, a fluid at low pressure and relatively high temp(with respect to the critical point) will be gaseous.  For gases following pv=RT, the enthalpy is strictly a function of tempeature. Therefore, with no change in enthalpy, there will be no change in temperature.

I believe Milton is correct only in the case of an ideal gas expanding through an isentropic nozzle.  The choke pressure is defined by a pressure ratio determined from the heat capacity ratio.  The temperature ratio is determined in an analagous relationship also depending on the heat capacity ratio.  So if only the inlet pressure is increased at sonic flow conditions the throat temperature (which is somewhat cooler than the inlet) would not change.   For an ideal gas, the sonic velocity can be fixed by a constant heat capacity ratio and temperature.  So the velocity does not increase but the mass flow rate increases because of the pressure change.

For a real gas, I guess that the throat temperature would increase (non-isentropic flow creating heat?).  So maybe for a real gas both velocity and mass flow rate would increase?

If you change any upstream conditon, you are changing the stagnation conditions and therefore have a new problem,For the perfect gas, for choking the critical pressure ratio will remain the same, however, the throat pressure, temperature and density will also change.  Since the throat temp will change, the acoustic velocity and hence throat velocity will change.

I still don't follow.  Let's assume initially that an ideal gas is flowing through an isentropic nozzle at choked conditions (sonic flow in the throat).   Now, increase only the inlet (stagnation) pressure but keep the inlet temperature the same.  The calculations will indicate, unless I have missed something, that the throat temperature does not change. The throat pressure does change (it increases).  So if sonic velocity is the same in both cases and choked flow occurs, wouldn't the velocity be the same in both cases?

      Adiabatic steady state perfect gas, constant specific heatsAo^2=kRTo =A^2+U^2(k-1)/2   (1)A^2=kRT   subscribt o refers to stagnation conditions

(P/Po)=(A/Ao)^(2k/[K-1])  (2)If local upstream source static temp is held contant and the upstream static pressure is increased, Po and Ao will change.If Po increases Ao will increase

At throat with choked flow the energy balance (1) yieldsAo^2=A^2 +A^(k-1)/2    =A^2(k+1)/2    Increased Ao yields increased A at throat.   Increased A at throat yields increase T static at throat.   Note stagnation temp is constant but has increased because of increased stag pressure at source.

Don't understand the use of A / Ao.   The case I am referring to is an isentropic nozzle with a fixed throat nozzle area.For an ideal gas / isentropic flow, the exit velocity (choked flow) is fixed by the discharge temperature and the heat capacity ratio (k) and is independent of the throat area.  The throat area does affect the mass flow rate but not the discharge velocity (choked flow only).So I still don't see how the velocity can change if the inlet temperature stays the same (choked conditions).

A/Ao=sqrt(T/To)A=sound speed   The subscript, o , for stagnation accounts for KE effectThe stagnation temp To is related to stagnation pressure by

(P/Po)=(T/To)^[k/(k-1)]  If static temp, T remains constant and either P or Po change, then To  and Ao change. From enery equation at choked conditions (Ao/A)^2=(k+1)/2With change in Ao, then A the throat velocity will change.

OK. An ideal gas is flowing through an isentropic nozzle at choked conditions.  We now increase the inlet pressure without changing the inlet temperature.  Does the throat velocity increase?

At choked conditions the pressure ratio (P/Po) does not change.  Also, the temperature ratio does not change.  If only the inlet pressure is increased this only changes the throat pressure but not the throat velocity which is determined by the throat temperature.  By your equation: 字串 9

A = Ao * sqrt(T/To)   

indicates that the throat velocity (choked) doesn't change if the temperature ratio doesn't change.

For an ideal gas, the sonic velocity = sqrt(kgRT).  The speed of sound at the inlet doesn't change if the temperature doesn't change.  You have increased the inlet pressure and therefore, while you have maintained, T as constant,  To, the stagnation temperature must increase. Ao must increase and the resulting energy equation yields an increase in the throat sound velocity.Regards

T.P-(1-1/k) = constant

If inlet pressure is increased and temperature remains the same, we have a different constant than before with lower inlet pressure.  Therefore, T and P at the throat will be different too.  Likewise, the speed of sound

c = sqrt(kgRT) = sqrt(kgP/ρ)

Temperature at throat (T*) (choked flow, ideal gas, isentropic) is:

T* = To*(2/(k+1)) ;  To = inlet stagnation temperature

Sonic Velocity is:

c* = sqrt(kRT*/Mw) ;

T* is only dependent on k and inlet temperature.  So sonic velocity doesn't change.  

The above from Perry's 7th edition page 6-23.

When the upstream pressure is increased, the Stagnation temperature increases.  For an adiabatic steady flow of perfect gas, the stagnation temp remains constant with the flow.  Use the energy equation with increased "stagnation" temperature and the resulting sonic velocity will increase.

or Ho=H +u^2/2    Cp(To-T)=u^2/2=a^2/2=kRT/2Since To increases, solve for T    I'm sorry, but you should be reading a good text, such as "Volume 1 of Shapiro" in compressible fluid flow. That type of text will clearly spell out that the upstream conditions are at stagnation.

Inlet temperature ≠ inlet stagnation temperature.

Stagnation temperature is the temperature the fluid would attain were it brought to rest adiabatically without the development of shaft work.

The more energy a stream has (i.e. higher pressure) the higher it's stagnation temperature. Good luck,Latexman

Are not the stagflation and inlet temperatures essentially the same when there is near zero approach velocity (in the case of a large tank with a hole)?   If you are arguing that this is never the case in real life then I see your point.  However, must release models/equations assume these conditions.   Of course, there is no ideal gas or isentropic flow in real life neither.   The stagnation and inlet temperature can be essentially the same when there is near zero approach velocity in a single pressure scenario.  However, your question was

An ideal gas is flowing through an isentropic nozzle at choked conditions.  We now increase the inlet pressure without changing the inlet temperature.  Does the throat velocity increase?

There were no qualifiers or specifications on how much the pressure was increased.  It's a question that needs a yes or no answer.  The correct answer is yes, the throat velocity increases.

'However, must release models/equations assume these conditions. "While Latexman has answered your original question", please note, that even with a perfect gas, those models are "quasi-steady". My response are based on steady state flow models.

I hope that these last responses have put to bed the incorrect perceptions relating to throat velocity not changing with the increased source pressure.

All my posts have been in reference to Milton's posting of the discharge equations above.  Sorry if I didn't make myself clear.  If one assumes the following:

1.  Isentropic flow through a nozzle (before and after)2.  The same ideal gas (before and after)3.  Heat capacity ratio doesn't change with temp / press4.  Large entrance area to nozzle area (stagnation temp = inlet temp) AND (stagnation pressure = inlet pressure) (before and after).  (No entrance pipe between stagnation zone and nozzle.) 字串 3

Throat velocity does not change with only an increase in the stagnation (also inlet pressure in this case) pressure.  The mass flow rate does increase.

If you are saying that there is a pipe between the stagnation zone and the nozzle where the pipe diameter is significant in comparison to the nozzle throat diameter, then that would be a different matter.

rbcoulter (Chemical)"Throat velocity does not change with only an increase in the stagnation (also inlet pressure in this case) pressure.??????  The mass flow rate does increase."

If stagnation pressure=inlet pressure,the stag temp=static temp, then throat velocity, mass flow remain fixed.

Case #1:

   1.  Po = Stagnation Pressure = Inlet Pressure       (inlet nozzle area is very large compared to throat)   2.  To =  Inlet temperature   3.  T* (throat temperature) = To*(2/(k+1))    4.  Throat velocity (choked) = c* = sqrt(kRT*/Mw)

Case #2:

   1.  2Po = Stagnation Pressure = Inlet Pressure       (inlet nozzle area is very large compared to throat)       (Pressure double of case #1)      2.  To =  Inlet temperature (same as Case #1)   3.  T* (throat temperature) = To*(2/(k+1)) (same as Case #1)   4.  Throat velocity (choked) = c* = sqrt(kRT*/Mw) (same Case #1)

Conclusion:

Case #1 and Case #2 have the same throat velocity (choked).What could I possibly be missing here?Is inlet nozzle area Case #1 = inlet nozzle area Case #2? Good luck,

Oh. So now I see your trick.

The inlet area is considered very large compared to the throat in both cases.   Trying to define a fixed inlet area does not work for this equation. May not sound realistic but it is my understanding that is the assumption behind the derivation of the equation.  

The inlet area is infinite in both cases.  The approach velocity is zero in both cases.     字串 8 Latexman (Chemical) 1 May 08 19:19 There's no trick.  Just defining the boundaries.

Inlet nozzle area Case #1 = ∞ = inlet nozzle area Case #2

Yes.  But neither is finite for this model.  If you try to get me to accept that then the model in invalidated and you can make your case.

I don't understand what that means.  I just want to establish that the only parameter or condition that changes from Case #1 to Case #2 is the inlet pressure.  Keep it simple. Good luck,

Yes. Only the inlet "stagnation" pressure changes with all the assumptions mentioned earlier.  This is "P" in Milton's equation which assumes a zero approach velocity.

It sounds like your trying to remove the constraint of zero approach velocity going from case #1 to case #2.  In this way you can claim that the kinetic energy of approach is greater in case #2 because of the higher pressure then saying that the stagnation temperature is higher and then that the throat temperature is higher then that the choke velocity is higher. This model doesn't allow for this (Milton's equations).  Other more realistic models may (please provide one or a reference).

My only point is that if you use Milton's equations, without deviating from the assumptions in which it was derived, then the choke velocity does not change if only "P" is increased.

"Miltons equations........"I believe the basic topic is steady state flow.The "accidental release" equations are at best an APPROXIMATION used in "quasi steady flow"Of course you can have a large container with a small break and approxmate zero velocity within the container. Initial conditions would set the starting(initial conditions) pressure and

tempearture.  The relation between the stagnation conditions would be related to heat transfer to the vessel and mass removed. For each step of the "quasi steady" analysis, "Miltons first equation can be used. (I question the second with regard to calculation of gamma),  However, I don't see how you are tying this in with sonic velocity other than the simple relation between the upstream and throat conditions of the flow.  Regarding the many references in this thread to "Milton's equations", I would like to make it clear that the equations I presented in this thread are not "my" equations. Although I have thoroughly checked their derivation, as stated above they are the equations given in: 字串 3

I could also add:

(4) Equations 5.20 and 5.21 on page 5-14 of the Sixth Edition of Perry's Chemical Engineers' Handbook, 1984. (Perry's equations include the local acceleration constant, g, because they are in the U.S. Customary units rather than SI Metric units).  

(5) For those of you who may be in the United Kingdom, exactly the same results are obtained by using Ramskill's equation. Ramskill, P.K., "Discharge Rate Calculation Methods for Use in Plant Safety Assessments", Safety and Reliability Directory, UK Atomic Energy Authority. 字串 1

I would also point out that the equations are not merely "accidental release" equations. As far back as the 1950's, when we were designing Exxon's Model IV fluid catalytic crackers in refineries, those equations were used to size the choked flow orifices that injected steam into the catalyst circulation system to fluidize the catalyst ... and if we needed to increase the mass flow rate of steam injection, we simply raised the inlet steam pressure. The point being that the equations I presented have been in use for over 60 years.

67 postings in this thread simply means it is an interesting subject...so go ahead! "We don't believe things because they are true, things are true because we believe them.""Small people talk about others, average people talk about things, smart people talk about ideas and legends never talk."