INTELLIGENT WORK FORUMS FOR ENGINEERING PROFESSIONALS
Log In
Come Join Us!
Are you an Engineering professional? Join EngTips Forums!
 Talk With Other Members
 Be Notified Of Responses
To Your Posts
 Keyword Search
 OneClick Access To Your
Favorite Forums
 Automated Signatures
On Your Posts
 Best Of All, It's Free!
 Students Click Here
*EngTips's functionality depends on members receiving email. By joining you are opting in to receive email.
Posting Guidelines
Promoting, selling, recruiting, coursework and thesis posting is forbidden. Students Click Here

Pipelines, Piping and Fluid Mechanics engineering FAQ
Choked mass flow rate of gases
Mass flow rate of a gas through an orifice during choked conditions by mbeychok
Posted: 26 Dec 05 (Edited 2 Feb 06)

. The velocity of a gas flowing through an orifice or an equipment leak attains a maximum or sonic velocity and becomes "choked" when the ratio of the absolute upstream pressure to the absolute downstream pressure is equal to or greater than [ ( k + 1 ) / 2 ]^{ k / ( k  1 )}, where k is the specific heat ratio of the gas. For many gases, k ranges from about 1.09 to 1.41, and therefore [ ( k + 1 ) / 2 ]^{ k / ( k  1 )} ranges from about 1.7 to about 1.9 ... which means that choked velocity usually occurs when the absolute upstream pressure is at least 1.7 to 1.9 times as high as the absolute downstream pressure.
In SI metric units, when the gas velocity is choked, the equation for the mass flow rate is:
or this equivalent form:
[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/s C = discharge coefficient (dimensionless, about 0.72) A = orifice hole area, m^{2} k = gas c_{p}/c_{v} = ratio of specific heats ρ = real gas density, kg/m^{3}, at upstream P and T P = absolute upstream pressure, Pa M = gas molecular weight (dimensionless) R = Universal Gas Law constant, (Pa)(m^{3} / (kgmol)(¦K) T = gas temperature, ¦K Z = the gas compressibility factor at P and T
When dealing with the choked flow of a gas through a leak hole in a pressurized gas system or vessel, it is important to realize that the above equations calculate the initial instantaneous mass flow rate for the pressure and temperature existing in the system or vessel when the release first occurs. The initial instantaneous flow rate from a leak in a pressurized gas system or vessel is much higher than the average flow rate during the overall release period because the pressure and flow rate decrease with time as the system or vessel empties. Calculating the flow rate versus time since the initiation of the leak is much more complicated, but more accurate. To learn how such calculations are performed, go to www.airdispersion.com/feature2.html.
When expressed in the customary USA units, the equations above also contain the gravitational conversion factor g_{c} which is 32.17 ft/s^{2} in USA units ... and since the factor g_{c} is 1 (kgm) / (Ns^{2}) in the SI metric system of units, the above equations do not include it.
The technical literature can be very confusing because many authors fail to explain whether they are using the Universal Gas Law constant R which applies to any ideal gas or whether they are using the gas law constant Rs which only applies to a specific individual gas. The relationship between the two constants is Rs = R / (MW).
Notes: (1) The above equations are for a real gas. (2) For an ideal gas, Z = 1 and d is the ideal gas density. (3) kgmol = kilogram mole
Milton Beychok (Visit me at www.airdispersion.com) 
Back to Pipelines, Piping and Fluid Mechanics engineering FAQ Index
Back to Pipelines, Piping and Fluid Mechanics engineering Forum 

Resources
What does it take to create innovative design for the most demanding industries? Download Now
Managing reverse logistics and depot repair, or all operations related to the reuse of products and materials, is a growing challenge for B2C and B2B manufacturers, retailers and service organizations. Download Now
Historically, fences and cages separated humans from machines. Robots were physically restricted and... Download Now
What is rapid injection molding? For engineers working with tight product design timelines, rapid injection molding can be a critical tool for prototyping and testing functional models. Download Now

