How does sonic flows maintain a steady flow rate if it does?
How does sonic flows maintain a steady flow rate if it does?
(OP)
I was wondering if anyone knows if a fluid that travels at sonic speeds in a pipe, or even supersonic speeds, maintain a constant flow rate, volume/time. If it does, can you please explain the mechanisms that it can. Also, I heard that steam, cannot be accelerated to speeds past Mach 1. If this is true or false, can you please explain this to me. I am researching the effects of a supersonic flow of steam for a steam generator, but I want to know the mechanism that are involved that ensure a steady flow rate, as I am told.
SalvadorT
SalvadorT





RE: How does sonic flows maintain a steady flow rate if it does?
However, once steady state, steady flow conditions prevail, the mass flow balance should hold, even if the volumetric flow rate is different from input to output.
RE: How does sonic flows maintain a steady flow rate if it does?
rmw
RE: How does sonic flows maintain a steady flow rate if it does?
In a pipe of constant diameter and assuming no heat transfer, a subsonic flow velocity will be proportional to the pressure differential between entry and exit of the pipe. Increasing the pressure differential will increase the fluid mass flow rate and as we are assuming incompressibility, the volumetric flow rate will be proportional, i.e. no change in density of the fluid. Now, due to the implicit relationship between cross sectional area and the mach number there is a critical mass flow rate at which the fluid becomes sonic, Ma=1. At this point the pipe or nozzle is said to be choked and further increases of pressure differential result in no further mass flow rate increase at the local sonic velocity. A choked pipe cannot exceed its local sonic velocity. The fluid starts to compress and become denser but not faster. The downstream pressure will become higher causing a backpressure to the system with a noticable associated temperature increase. The only method of increasing the velocity of the fluid further is to allow a controlled expansion of the fluid by increasing the area ratio between throat or pipe and its exit, however the mass flow rate will now be constant regardless of the new higher exit velocity. If the fluid is allowed to expand too quickly, termed 'over-expansion' there will be a sudden deceleration and pressure increases seen as a result of the formation of a series of 'normal shocks' until the fluid has been expanded across these shocks to the exit conditions. Conversely, under-expansion will just decelerate the flow back to sonic or subsonic but with the possible formation of 'normal shock', prantyl meyer waves and viscous damping effects seen as rapid pressure fluctuations or pressure pulsing which will effect the pipe flow far upstream and will in fact cause fluctuations in the volumetric flow rate as the flow would tend towards transonic. To change the required constant mass flow rate of a system yet maintain sonic conditions would require a larger diameter pipe as determined by the area/mach number relationship.
So to answer your questions, subsonic mass flow rate will keep increasing as the pressure difference is increased until the pipe is choked at which point mass flow rate remains constant this will correspond to the a local fluid velocity of Ma=1 which cannot be exceeded. Further increase of the inlet pressure will simply start compressing the fluid and increasing the effective backpressure i.e. a change in fluid density. To accelerate the fluid to velocities greater than Ma=1 the pipe would need to change area as a function of the mach number and the effective back pressure controlled to maintain the flow without the formation of Normal Shocks causing rapid deceleration.
Tip: Design for constant mass flow not volumetric flow !!!!
RE: How does sonic flows maintain a steady flow rate if it does?
Flow in pipes cannot be supersonic. Flow in pipes is described in the section of most compressible flow texts under the heading of "flow in long ducts", or something to that effect. The common point being long channels of constant cross-section. Fanno Lines describe the non-dimensionalized relationships for such flow.
"Axiomatrix" well-described some of the phenomena of nozzle flows. The main point being that the maximum mass flow per unit area is determined for a given set of upstream conditions. If the pressure ratio across a nozzle exceeds the "critical pressure ratio" (i.e. "choked" flow, or sonic velocity in the throat) , then the unit mass flow will NOT increase, but the exit velocity may increase beyond the sonic velocity if the nozzle is properly designed as a converging/diverging nozzle.
RE: How does sonic flows maintain a steady flow rate if it does?
RE: How does sonic flows maintain a steady flow rate if it does?
RE: How does sonic flows maintain a steady flow rate if it does?
For a compressible fluid such as steam flowing adiabatically ( no heat transfer) thru a fixed geometry orifice or pipe , the flow may choke acoustically thru a flow area minimum or it can also be choked frictionally ( a long pipe ,so-called Fanno flow).
The flow relationship will be fixed for a fixed area, geometry , inlet pressure,specific compressible fluid and inlet temperature. Once the flow parameters have been determined by a flow test or CFD analysis ( to account for oblique shock waves). For any flow for parameters other than the test parameters, the flow can be prorated up directly proportional to inlet pressure and up directly proportional to the square root of the absolute inlet temperature.
As others have stated, it is neccesary for the pressure drop to be greater than the critical drop in order to have choked flow, which can be predicted once the fluid's ratio of heat capacities is known ( R= Cp/Cv)
RE: How does sonic flows maintain a steady flow rate if it does?
When a gas flow is at "choked" conditions (i.e., at sonic velocity), the LINEAR VELOCITY IS AT A MAXIMUM. By linear velocity, I mean ft/sec or m/sec for example.
However, at "choked" conditions, the MASS FLOW RATE IS NOT AT A MAXIMUM. Increasing the upstream pressure will continue to increase the mass flow rate. By mass flow rate, I mean pounds/sec or kilograms/sec for example.
Milton Beychok
mbeychok@xxx.net (replace xxx with cox)
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
One point that is missing is that sonic flow is not sustainable in straight pipe. Period. If you enter a pipe at sonic velocity (downstream of a choke for example), friction effects will begin to reduce the velocity immediately and the duration of M=1.0 is meters, not kilometers or even tens of meters.
The Continuity Equation explains that a system with one inlet and one outlet must have exactly the same mass flow rate at the inlet, at the outlet, and at every point between the inlet and the outlet. Any other answer would result in fluids "stacking up" at various points within the system -- a non-tenable situation. Therefore, as the pressure and temperature change across a system, the velocity will change, the volume-flow rate will change, and the mass flow rate will remain constant at every cross section in the system.
A non-zero "constant volume flow rate" with regard to time is not possible. Volume flow rate (in actual terms) is a function of pressure, temperature and compressibility. If pressure does not change with distance from a starting point, then there is zero flow. If you are talking about a "constant volume flow rate at standard conditions" then the "volume flow rate" is really a mass flow rate re-stated in volumetric units.
Supersonic flow is very difficult to acheive, is very energy-intensive to sustain, and will not occur without specifically engineered equipment. Take a look at the specifications for supersonic aircraft. Specifically look at the hp requirement and the fuel-consumption at subsonic and supersonic speeds. The difference is remarkable.
David Simpson, PE
MuleShoe Engineering
www.muleshoe-eng.com
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
The Plural of "anecdote" is not "data"
RE: How does sonic flows maintain a steady flow rate if it does?
WRITES
However, at "choked" conditions, the MASS FLOW RATE IS NOT AT A MAXIMUM. Increasing the upstream pressure will continue to increase the mass flow rate. By mass flow rate, I mean pounds/sec or kilograms/sec for example.
I disagree. Choked flow in steady state refers to the maximum mass flux. For a perfect gas, this occurs at Mach=1.
For an adiabatic pipe, for which exit conditions are sonic, further increasing the upstream pressure will increase the mass flux, however, the exit condition will remain at Mach=1.
Similarly, if the flow is via a variable area, choking occurs at the max mass flux.
To calculate choked two phase single component flow from an adiabatic pipe, one calculates mass flux vs exit pressure. As exit pressurea drops mass flux increases until a max is reached.
That is the condition for choked flow.
RE: How does sonic flows maintain a steady flow rate if it does?
One point that is missing is that sonic flow is not sustainable in straight pipe. Period. If you enter a pipe at sonic velocity (downstream of a choke for example), friction effects will begin to reduce the velocity immediately and the duration of M=1.0 is meters, not kilometers or even tens of meters.
It is not clear to this writer how in steady adiabatic flow the entrance Mach=1 for a pipe. Unless the pipe length is exactly zero length. Greater or less than M=1.0 is clear to me. Am I misunderstanding how the FANNO line works?
RE: How does sonic flows maintain a steady flow rate if it does?
The equation (in SI metric units) for calculating the mass flow rate of a gas across a restriction orifice at choked conditions is:
Q = C A P [ k M / ( R T ) ]1/2 [ 2 / ( k + 1 ) ] (k + 1) / (2k - 2)
where:
Q = mass flow rate of the gas, kg/s
C = discharge coefficient
A = discharge hole area, m2
P = absolute upstream pressure, Pa
k = Cp / Cv of the gas
M = gas molecular weight
R = Universal Gas Law constant = 8314.5 ( Pa ) ( m3) / ( kgmol ) ( deg K )
T = gas temperature, deg K
The same equation in customary USA units is:
Q = C A P [ g k M / ( R T ) ]1/2 [ 2 / ( k + 1 ) ] (k + 1) / (2k - 2)
where:
Q = mass flow rate of the gas, lb/s
C = discharge coefficient
A = discharge hole area, ft2
P = absolute upstream pressure, lb/ft2
g = gravitational acceleration of 32.17 ft/s2
k = Cp / Cv of the gas
M = gas molecular weight
R = Universal Gas Law constant = 1545.3 ( ft-lb ) / ( lbmol ) ( deg R )
T = gas temperature, deg R
As can be seen in the above equation, increasing the upstream gas pressure increases the mass flow rate (even at choked flow conditions).
A careful reading of the following web sites will confirm what I have said:
(1) http://www.okcc.com/PDF/Choked.pdf
(2) http:/
(3) http://w
The above reference web site (2) presents the choked flow equation in an equivalent but different form, which still shows that increasing the upstream gas pressure increases the mass flow even at choked conditions.
The above reference web site (3) also presents the choked gas flow equation in an equivalent but different form and it also shows that increasing the upstream gas pressure increases the mass flow even at choked conditions.
I am sure that you can also find confirmation of what I said in any good chemical engineering textbook on fluid flow.
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
Q = C A P [ g k M / ( R T ) ]1/2 [ 2 / ( k + 1 ) ] (k + 1) / (2k - 2)
As can be seen in the above equation, increasing the upstream gas pressure increases the mass flow rate (even at choked flow conditions).
PLEASE NOTE: FIX THE UPSTREAM PRESSURE SUCH AS P IN THE ABOVE EQUATION. THEN DECREASE THE BACK PRESSURE UNTIL THE FLOW CHOKES--THAT IS REACHES A MAX. CHECK THE MACH NO AT THE CHOKED FLOW-IT SHOULD BE M=1. OF COURSE AN INCRESASE IN SOURCE PRESSURE WILL INCREASE THE FLOW, IF IT HAD BEEN PREVIOUSLY CHOKED. HOWEVER, AT THE MINIMUM AREA WHERE THE FLOW IS CHOKED AT A NEW FLOW RATE, THE MACH NO. IS STILL UNITY.
RE: How does sonic flows maintain a steady flow rate if it does?
Quote from your response of Nov.11th:
"OF COURSE AN INCREASE IN SOURCE PRESSURE WILL INCREASE THE FLOW, IF IT HAD BEEN PREVIOUSLY CHOKED. HOWEVER, AT THE MINIMUM AREA WHERE THE FLOW IS CHOKED AT A NEW FLOW RATE, THE MACH NO. IS STILL UNITY."
Quote from your response of Aug.6th:
"If the critical pressure ratio is exceeded, the downstream conditions will be choked (M=1). However, if the upsteam pressure is further increased the mass flow will increase. Further reducing the downstream pressure will not increase the mass flow."
Quote from my posting of November 8th:
"When a gas flow is at "choked" conditions (i.e., at sonic velocity), the LINEAR VELOCITY IS AT A MAXIMUM. By linear velocity, I mean ft/sec or m/sec for example.
However, at "choked" conditions, the MASS FLOW RATE IS NOT AT A MAXIMUM. Increasing the upstream pressure will continue to increase the mass flow rate. By mass flow rate, I mean pounds/sec or kilograms/sec for example."
We are both saying the same thing. On Nov.8th, I said that at choked conditions, the linear velocity is at a maximum (i.e. the linear velocity is at sonic velocity which is M=1) but increasing the upstream pressure will still increase the mass flow. In other words, the meters/sec or feet/sec is at a maximum but increasing the upstream pressure will still increase the kilograms/sec or pounds/sec.
Isn't that exactly what you said on Aug. 6th and Nov. 11th? So I am at a loss as to why you disagreed with what I said on Nov. 8th.
I think the problem is that mechanical engineers tend to use the terminology "mach number=1" which means that the linear velocity is at the speed of sound, and we chemical engineers use the terminology "sonic velocity" which also means the linear velocity is at the speed of sound.
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
My disagreement is with the statement that "However, at "choked" conditions, the MASS FLOW RATE IS NOT AT A MAXIMUM.
Choked flow means that mass flux is a maximum. Further increasing upstream pressure, etc. will increase flux, however, with the new source pressure, lowering back pressure will not further increase flux.
RE: How does sonic flows maintain a steady flow rate if it does?
One more time and then I quit!! Choked flow does not mean that the mass flow (kg/sec) is at a maximum ... it means that the linear velocity (m/sec) is at a maximum (i.e., the linear velocity is at Mach=1). Yes, lowering the downstream pressure will not increase the mass flow but increasing the upstream pressure will do so. The very fact that you can increase the mass flow by increasing the upstream pressure proves that the mass flow is not at a maximum.
Mass flow equals the gas linear velocity times the cross-sectional area times the gas density ... (m/s)(m2)(kg/m3] = kg/s ... increasing the upstream pressure increases the gas density and that increases the mass flow even though the linear velocity is at a maximum.
Milton Beychok
mbeychok@xxx.net (replace xxx with cox)
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
htt
The compressibility effects on mass flow rate have some unexpected results. We can increase the mass flow through a tube by increasing the area, increasing the total pressure, or decreasing the total temperature. But the effect of increasing velocity (Mach number) is a little harder to figure out. If we were to fix the area, total pressure and temperature, and graph the variation of mass flow rate with Mach number, we would find that a limiting maximum value occurs at Mach number equal to one. Using calculus, we can mathematically determine the same result: there is a maximum airflow limit that occurs when the Mach number is equal to one. The limiting of the mass flow rate is called choking of the flow. An equation for the choked mass flow rate is given below the box.
mdot = (A* * pt/sqrt[Tt]) * sqrt(g/R) * [(g+1)/2]^-[(g+1)/(g-1)/2]
RE: How does sonic flows maintain a steady flow rate if it does?
As I said in my very first posting to this thread on Nov. 8th, the point I made is often mis-stated and/or mis-understood ... and that includes NASA as well as many others. Go back through all of my posts and think it through for yourself!!
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
Nozzles don't have the limitations of cylindrical pipes, limitations caused by their constant cross-sectional areas. As said above by various contributors properly designed nozzles enable the interchange of internal and kinetic energy of a fluid as a result of the changing cross-sectional area.
Steam turbines or, for example, ammonia or ethylene expanders, have alternate sets of nozzles and rotating blades through which vapor or gas flow in a steady-state expansion process whose overall effect is the efficient conversion of the internal energy of a high-pressure stream into shaft work.
For subsonic flows in a converging nozzle pressure decreases and velocity increases as the cross-sectional area diminishes. The speed of sound, the maximum attainable speed, is reached at the throat. To allow the speeds to become supersonic and the pressure to drop further would require an increase in cross-sectional area, a diverging section, as in the diffusers of steam ejectors.
To SalvadorT. In short: a converging nozzle can be used to deliver a constant flow rate (at a given P1 upstream pressure) of a compressible fluid into a region of variable pressure by reducing the downstream pressure P2, so the ratio to upstream pressure is below a critical value, which for steam is ~0.55 at moderate temperatures and pressures.
The flow remains constant, and the velocity in the throat sonic, regardless of the P2/P1 ratio as long as it stays below the critical value.
RE: How does sonic flows maintain a steady flow rate if it does?
Flow in pipes cannot be supersonic. Flow in pipes is described in the section of most compressible flow texts under the heading of "flow in long ducts", or something to that effect. The common point being long channels of constant cross-section. Fanno Lines describe the non-dimensionalized relationships for such flow.
Flow in pipes CAN be supersonic. With M>1 the Mach no tends to decrease in the flow direction towards M=1. Refer to any compressible flow text AND THE FANNO LINE. Dependent upon friction and back pressure conditions, a shock can occur. The dowstream flow conditions are then subsonic with the Mach No. increasing towards M=1.
RE: How does sonic flows maintain a steady flow rate if it does?
Mach number is a ratio of the local fluid velocity to that of the sound speed (of that medium of course). Of course steam can be accelerated to supersonic conditions.
Most of the thread discussion seems to be centered on steady state adiabatic flow.
It is interesting to note thata perfect gas, with constant specific heats under isothermal conditions,---- flow in a long duct will choke at a Mach No. of 1/sqrt(gamma. Where gamma is the ratio of the specific heats, Cp/Cv.
RE: How does sonic flows maintain a steady flow rate if it does?
"mbeychok":
If one increases the upstream pressure, one has changed the conditions of the flow "problem" under consideration. Of course the mass flow can be increased if the upstream pressure is increased, you are absolutely right, but missing part of the point that others have been making.
The phrase "choked flow" implicitly refers to fixed upstream conditions. This is not something to agree with, or disagree with; it is simply the convention for that expression.
Part of this depends upon one's point of view at a flow nozzle, orifice, etc. Terminology within a particular specialty of engineering might reflect a point of view that is either upstream or downstream, and seems to differently describe identical phenomena.
Some turbine manufacturers, for example, refer to flow through a row of (converging) airfoil nozzles as "restricted flow" if the throat velocity is at the local sonic velocity; the mass flow cannot be increased by increasing any of the downstream areas or pressures in the flow path because the sonic flow point represents a "restriction" in the flow FOR A GIVEN SET OF UPSTREAM CONDITIONS. Similarly, it is called "unrestricted flow" if the nozzle exit flow is at a velocity less than the local sonic velocity. One could think of it as "not yet limited" flow, rather than "unrestricted" flow. IT IS UNDERSTOOD THAT THE MASS FLOW COULD BE INCREASED - if the upstream pressure was increased, but that is not necessarily the objective.
RE: How does sonic flows maintain a steady flow rate if it does?
Quote from your posting of Nov.13:
"The phrase "choked flow" implicitly refers to fixed upstream conditions. This is not something to agree with, or disagree with; it is simply the convention for that expression."
Thank you for your very reasoned posting. Actually, I am not missing the point others make and I fully understand that choked flow implicitly refers to fixed upstream condition ... but only for some people wotking in some disciplines. Restriction orifices are very often used at choked velocity conditions as mass flow controllers. For example, when one wants to inject a constant mass flow of steam into a process vessel in a petroleum refinery or petrochemical plant and wants that flow to be constant even though the downstream pressure (i.e., inside the vessel) may not be constant. In that case, the upstream steam pressure is controlled at a pressure high enough to insure that choked conditions prevail in the flow through the orifice. If, for some reason, one wants to increase that constant mass flow amount (say from 100 kg/s to 150 kg/sec), then one simply controls the upstream steam at a higher pressure. In such such cases, the process designer does not implicitly assume any convention about choked flow referring to fixed upstream conditions. He knows that, at choked conditions, the mass flow is not at a maximum even though the gas velocity is at a maximum. That is common knowledge in everyday use for a process design engineer in the hydrocarbon processing industries (oil refineries, natural gas plants and petrochemical plants). As said by Flareman (Petroleum) in Thread378-25153: "the actual pressure influences the true mass flow and there is no "maximum" flow, just a maximum velocity".
Please take just a few minutes to read the tutorial at http://www.okcc.com/PDF/Choked.pdf and you will see that there is an entirely different mindset in other disciplines.
My philosophy:
I firmly believe that whenever one publishes a technical paper or posts a message in a technical forum such as this, one must realize that the paper or message must be understood by a universe of people in disciplines other than that of the writer. For example, a NASA engineer publishing a treatise on fluid mechanics on the Internet should keep in mind that people other than aeronautic engineers or rocket designers may be reading his treatise ... and not all of the readers accept the convention that choked flow refers to fixed upstream conditions. Nor should one use the gas constant R without explaining that it is the specific gas constant for air rather than the universal gas constant (since the specific constant R equals the universal gas constant divided by the gas molecular weight) ... his aeronautic engineering colleagues may understand what he has done, but other engineers will wonder why the molecular weight has disppeared because they deal with many gases other than air.
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
The equation (in SI metric units) for calculating the mass flow rate of a gas across a restriction orifice at choked conditions is:
Q = C A P [ k M / ( R T ) ]1/2 [ 2 / ( k + 1 ) ] (k + 1) / (2k - 2)
where:
Q = mass flow rate of the gas, kg/s
C = discharge coefficient
A = discharge hole area, m2
P = absolute upstream pressure, Pa
k = Cp / Cv of the gas
M = gas molecular weight
R = Universal Gas Law constant = 8314.5 ( Pa ) ( m3) / ( kgmol ) ( deg K )
T = gas temperature, deg K
One should be careful on the use of what can be static and stagnation conditions.
The above formula P and T must be taken at stagnation conditions, not that of local static pressure and temperature. ---UNLESS THE FLOW IS FROM AN INFINITE RESERVOIR FEEDING DIRECTLY INTO A RESTRICTION FROM THE RESERVOIR. In that case stagnation conditions and static conditions are the same.
Of course the above results are for perfect gas, constant specific heats.
RE: How does sonic flows maintain a steady flow rate if it does?
If you are going to copy and quote the equation that I posted for the choked flow of a gas through an orifice, then you should really learn how to display the superscript parameters (which you have not done). So I will again provide the equation in its correct form:
Q = C A P [ k M / ( R T ) ]1/2 [ 2 / ( k + 1 ) ] (k + 1) / (2k - 2)
where:
Q = mass flow rate of the gas, kg/s
C = discharge coefficient
A = discharge hole area, m2
P = absolute upstream pressure, Pa
k = Cp / Cv of the gas
M = gas molecular weight
R = Universal Gas Law constant = 8314.5 ( Pa ) ( m3) / ( kgmol ) ( deg K )
T = gas temperature, deg K
The pressure (P) and temperature (T) are very plainly and simply the conditions upstream of the orifice (i.e., at the inlet to the orifice). There is absolutely no need to use the terms "stagnation conditions" and "local static pressure". Anyone who can read English will readily understand "upstream" or "inlet". So why introduce unnecessary and confusing technical jargon ... especially when you don't define the meaning of the terms?
Yes, the equation was derived for an ideal gas and it has been in widespread use as such for the last 50 to 60 years to calculate the mass flow rate of a gas through an orifice at choked conditions. If non-ideality is of concern (and it rarely is), then it is very easy to introduce the compressibility factor (Z) of the gas into the equation.
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
Stagnation is sometimes refered to as Total
alpha= (k-1)/2 M= Mach No.
Tstagnation=T(1+alpha*M^2)
Pstagnation= P(1+alpha*M^2)^[k/(k-1)]
Where P and T are the local static upstream conditions.
Use of static pressure and temperature will obviously give error. IF UPSTREAM MACH=0, EQUATION OF MBEYCHOK IS SATISFACTORY.
If fluid is flowing such as in a pipe to an orifice then stagnation conditions must be accounted for in mass flow equations. THEN SIMPLY SUBSTITUTE Pstagnation and Tstagnation for p and T.
See and text such as:
The Dynamics and Thermodynamics of Compressible Fluid Flow by Ascher H. Shapiro
Gas Tables by Keenan and Kaye
Elements of Gas Dynamics by Lepmann and Roshko.
RE: How does sonic flows maintain a steady flow rate if it does?
The test sections in these tunnels are supposed to have upstream and downstream combinations of converging/diverging nozzles to create and maintain supersonic velocities.
RE: How does sonic flows maintain a steady flow rate if it does?
Thanks for your apology for mis-copying the equation that I posted, which you refer to as "the mbeychok equation". It is not my equation ... it has been available in "Perry's Chemical Engineers' Handbook" and other textbooks for the past 50-60 years. In my Sixth Edition of Perry's, it appears on page 5-14 as equation 5-21.
Milt Beychok
RE: How does sonic flows maintain a steady flow rate if it does?
This little tempest in a teapot is amusing - for a few posts, anyway
Let the tempest pass. If Perry's Chemical Engineers' Handbook" uses an equation implying p and T as upstream pressures without qualifying these parameters as stagnation conditions, then the quoted equation is quoted wrong. With movement of the fluid upstream of the orifice, nozzle, etc,the total pressure and temp has to include the kinetic energy of the fluid.
That is my last word on proper use of static and stagnation conditions.
RE: How does sonic flows maintain a steady flow rate if it does?
I am not trying to be facetious, but I simply don't understand what you said:
Let us assume that we have a gas in a pipe and the gas is flowing through a restriction orifice installed in the pipe. If we also have a pressure gauge installed in the pipe just upstream of the orifice and that pressure gauge tells us that the actual, measured pressure is 100 psig (114.7 psia), are you saying that we cannot use that pressure as the orifice inlet pressure unless we qualify it as the "stagnant" pressure or the "total pressure" or that it does or does not include the "kinetic energy" of the flowing gas? In my mind, that pressure read by the pressure gauge is the actual upstream pressure of the gas entering the restriction orifice ... and we need not qualify as anything but the actual pressure.
RE: How does sonic flows maintain a steady flow rate if it does?
In your example of 114.7 psia, if the pressure is static, via say a regular bordon tube gage and the gas air, k=1.4
Then p/pstag =0.99303 if M=.1 and T/Tstag=0.998
p/pstag=0.93947 if M=0.3 T/Tstag=0.98232
p/pstag=0.843 M=0.5 T/Tstag=0.952
The equation quoted from Chem Engrs Hand Book should be using Pstag and Tstag as the upstream press and temp.
Having the upstream Mach no. with a known static temp and press allows calc of pstag and Tstag. Derving the mass flow equation from consv of energy and mass will show that stagnation conditions satisfy the quoted equation.
RE: How does sonic flows maintain a steady flow rate if it does?
I think perhaps I am beginning to understand the problem you and I have communicating on the subject of this thread. In chemical manufacturing plants, steam generating plants, oil refineries, natural gas processing, and so forth there would rarely be gas flowing in pipes at velocities exceeding 120 ft/sec (36.6 m/sec). At gas velocities above that, the piping would undergo severe erosion/corrosion problems.
If, for example, we consider natural gas (essentially methane) flowing in a pipe at say 20 deg C, the sonic velocity in methane at that temperature is about 447 m/sec. Therefore, the Mach number of methane flowing at 36.6 m/sec would only be 36.6/447 = 0.08 and at that Mach number (according to your last posting) the difference between the pressure measured by a pressure gauge and what you call stagnation pressure would be a good bit less than 1 percent. So I guess that aeronautical engineers and rocket designers just work in an entirely different realm than we chemical engineers. We just don't deal with gases flowing at Mach numbers above 0.01 in designing industrial process plants. This not to say that I agree totally with you, but I am beginning to see that we just don't speak the same language.
Milton Beychok
(Visit me at www.air-dispersion.com)
RE: How does sonic flows maintain a steady flow rate if it does?
M flow %error
0.1 0.6
0.3 5.2
0.5 13.6
In the nuclear industry, one considers high energy line breaks and the calculations are required to be as accurate as possible.
With extremely low Mach Nos, the flow with LOW pressure drop can be approximated as incompressible. However, when dealing with compressible flow, one must be aware of the impact of compressibility.
For example:
----For transient flow, some enginers have thought that flow chokes at the critical pressure ratio used in steady state (which is not true)
----I don't believe placing Z in the Chem Eng. Hand Bk formula is not enough to compensate for High pressure and low temp gases. The orig derivation of the mass flow is based on an energy balance which requires input of enthalpy, which in turn is a function of Z.
If I were to deal with gases which deviated significantly from the perfect or with specific heats that varied significantly with Temp (Hand Bk assumes constant spec heats), my pencil, paper and table of integrals (for enthalph derivation) would come out. Possibly I would have to use numerical integration.
RE: How does sonic flows maintain a steady flow rate if it does?
The stagnation properties can also be estimated from the free-stream velocity Vo, as follows:
Tstag=To + Vo2/(2gccpJ)
pstag=po+(ρoVo2/2gc)[1 + Mao2/4 + (2-γ) Mao2/24 +...]
From the second formula one sees that for incompressible fluids, the stagnation pressure at low Mach numbers is reducible to the sum of the static pressure and the velocity pressure which chem. engineers are well acquainted with.
In order to get an idea of the values of Mao, the sonic velocity of dry and superheated steam is in the order of 2000 fps.
Notation:
Mao: the free-stream Mach number. The Mach number is also a measure of the ratio of the inertial force to the elastic force and a measure of the kinetic energy to the internal energy.
gc: gravitational conversion factor
cp: specific heat
J: the mechanical equivalent of heat
ρo: the free-stream gas density; the stagnation density can be estimated from the stagnation pressure and temperature ρstag=pstag/RTstag, where R is the specific gas constant.
γ: Cp/Cv
BTW, there are indeed industrial uses for sonic velocities, as when designing safety relief valves, control valves, flares, steam generating plants, steam ejectors, reducing orifices, etc.
As an aside, in hypersonic wind tunnels, air flows at speeds roughly in the range of 5 to 15 times the speed of sound !
RE: How does sonic flows maintain a steady flow rate if it does?
pstag=po+(?oVo2/2gc)[1 + Mao2/4 + (2-?) Mao2/24 +...]
I don't disagree with this approximation. However, I believe that definition relating static to stag pressure is for isentropic flow. Perhaps I am wrong.
I'm interested in seeing how this approximation is derived for non-isentropic flows.
RE: How does sonic flows maintain a steady flow rate if it does?
The above "series-type" approximation formula was taken from Chapter 2, "Fluid Flow", under the heading: Stagnation Properties in Fan Engineering by the Buffalo Forge Company, eighth (1983) edition. Edited by Robert Jorgensen.
RE: How does sonic flows maintain a steady flow rate if it does?
RE: How does sonic flows maintain a steady flow rate if it does?
Left click the Process TGML link and read.
Good luck,
Latexman
RE: How does sonic flows maintain a steady flow rate if it does?
Sent: Thursday, February 24, 2005 4:06 PM
To: Reed, Dorise
Cc: cab4@nrc.gov; fred moody; pvanstol@bechtel.com
Subject: handboook error
Ms. Reed,
Please refer to the Standard Handbook for Mechanical Engineers-Baumister& Marks, Seventh Edition pg 4-62
The reference page includes formulas for orifice computations. The formulas for the mass flow, m, in particular for choked flow (being independent of downstream pressure) indicate dependence on pressures of p(subscript1) and T(subscript1) where the subsripts refer to the static pressure and temperature and a particular section.
The pressure and temperature refered to in the handbook should be refered to as stagnation pressure and temperatures at the corresponding section of upstream flow.
The formulas are for a perfect gas with constant specific heat. Using the static conditions in place of stagnation will lead to error in computation of mass flow rates for choked flow.
I believe the same type of formula with error is given in your Chemical Engineers Handbook and more recent editions of the Mechanical Engineers Handbook.
Sincerely
RE: How does sonic flows maintain a steady flow rate if it does?
Subject: RE: handboook error
Date: Wed, 2 Mar 2005 10:12:09 -0500
From: "Prof_CS, College" <College_Prof_cs@mcgraw-hill.com>
Dear Customer,
Thanks for your inquiry. We did forward your comments to our editorial department, who agreed that the updates need to be made and will appear in the next edition. We value customer feedback such as yours. Thanks again for your correspondence.
Sincerely,
McGraw Hill Customer Service
-----Original Message-----
From: Reed, Dorise
Sent: Wednesday, March 02, 2005 9:15 AM
To: Day, Kimberly
Subject: FW: handboook error
Editoral request.
RE: How does sonic flows maintain a steady flow rate if it does?
dorise_reed@ mcgraw-hill.com