INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS
Log In
Come Join Us!
Are you an
Engineering professional?
Join Eng-Tips Forums!
- Talk With Other Members
- Be Notified Of Responses
To Your Posts
- Keyword Search
- One-Click Access To Your
Favorite Forums
- Automated Signatures
On Your Posts
- Best Of All, It's Free!
- Students Click Here
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.
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, m2
k = gas cp/cv = ratio of specific heats
ρ = real gas density, kg/m3, at upstream P and T
P = absolute upstream pressure, Pa
M = gas molecular weight (dimensionless)
R = Universal Gas Law constant, (Pa)(m3 / (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.air-dispersion.com/feature2.html.
When expressed in the customary USA units, the equations above also contain the gravitational conversion factor gc which is 32.17 ft/s2 in USA units ... and since the factor gc is 1 (kg-m) / (N-s2) 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.air-dispersion.com) |
Back to Pipelines, Piping and Fluid Mechanics engineering FAQ Index
Back to Pipelines, Piping and Fluid Mechanics engineering Forum
|
|
Resources
Today’s aerospace and defense companies are at the forefront of two historic trends: unprecedented innovation and increased complexity. A&D companies must embrace the digital enterprise in order to be more productive, innovate faster, and achieve program execution excellence to ensure programs deliver on technical requirements, cost and schedule. Download NowLimits placed on how many workers can gather at a job site vary, but these physical distancing directives can be overcome with augmented and virtual reality (AR and VR) technology. AR and VR can transport key people to any job site, opening up the site and allowing more people to be on-site virtually, without requiring travel or risky physical interaction. Download NowData collection has always been crucial for the oil and gas industry, but it once required a team of multiple technicians carrying clipboards and tape measures to perform data recording in the field by hand. This engineering.com whitepaper explores how 3D laser scanning can be used in the oil and gas sector. Download NowAs the world demands higher performance, higher bandwidth, and greater capacity from smaller, lighter, and lower-power products, high-density advanced packaging (HDAP) becomes a design necessity. Learn what's required to build a true, multi-substrate flow for emerging HDAP design requirements. Download Now
|
|
Talk To Other Members