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 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)
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