Machine Design

How-to, in-depth technical articles for machine design engineers

Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

Autonomous Vehicle Engineering

The No. 1 media source for those developing the next generation mobility solutions.

more free magazines
List Recent Topics | Start a New Topic
 

<< Previous Message No. 16827 Next >>
Author: mbeychok
Time: 09/30/05 19:40 PST
Reply | Original Message | New Topic | List Topics | List Messages on This Topic
Current Topic:
Equations for choked flow of gases
The subject of gas flow through orifices, especially under sonic velocity conditions (i.e., choked flow) , is very often raised in engineering discussion forums.  The following material should be helpful for many of you.

SI Metric Units

The velocity of gas flowing through an orifice becomes choked (and is also referred to as sonic velocity) 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 discharged gas.  For many gases, k ranges from about 1.09 to about 1.41, and thus [ ( k + 1 ) / 2 ] k / ( k - 1 ) ranges from 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 the SI Metric units, when the gas velocity is choked, the equation for the mass flow rate is:

Q = C A [k d P]1/2[2/(k+1)](k+1)/(2k-2)

or this equivalent form:

Q = C A P[k M/(R T)]1/2[2/(k+1)](k+1)/(2k-2)

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 source pressure is increased.

Q = mass flow rate, kg/s
C = discharge coefficient (dimensionless, usually about 0.72)
A = discharge hole area, m2
k = gas cp/cv = (specific heat at constant pressure)/(specific heat at constant volume)
d = gas density, kg/m3, at upstream pressure
P = absolute upstream pressure, Pa
M = gas molecular weight
R = the Universal Gas Law Constant = 8314.5 (Pa)(m3)/(kgmol)(°K )
T = gas temperature, °K

USA Units

The velocity of gas flowing through an orifice becomes choked (and is also referred to as sonic velocity) 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 discharged gas.  For many gases, k ranges from about 1.09 to about 1.41, and thus [ ( k + 1 ) / 2 ] k / ( k - 1 ) ranges from 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 the customary units used in the USA, when the gas velocity is choked, the equation for the mass flow rate is:

Q = C A [g k d P]1/2[2/(k+1)](k+1)/(2k-2)

or this equivalent form:

Q = C A P[g k M/(R T)]1/2[2/(k+1)](k+1)/(2k-2)

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 source pressure is increased.

Q = mass flow rate, lb/s
C = discharge coefficient (dimensionless, usually about 0.72)
A = discharge hole area, ft2
g = gravitational acceleration of 32.17 ft/s2
k = gas cp/cv = (specific heat at constant pressure)/(specific heat at constant volume)
d = gas density, lb/ft3, at upstream pressure
P = absolute upstream pressure, lb/ft2
M = gas molecular weight
R = the Universal Gas Law Constant = 1545.3 (ft-lb)/(lbmol)(°R )
T = gas temperature, °R

Milton Beychok
(Visit me at www.air-dispersion.com)

[ List Replies to This Message Only ]
Glossary