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When gas stored under pressure in a closed vessel is discharged to the atmosphere through a hole or other opening, the gas velocity through that opening may be choked (i.e., has attained a maximum) or nonchoked. Choked velocity, which is also referred to as sonic velocity, occurs when the ratio of the absolute source pressure to the absolute downstream ambient 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 source vessel pressure is at least 1.7 to 1.9 times as high as the absolute ambient atmospheric pressure.
When the gas velocity is choked, the equation for the mass flow rate is:[ It is important to note that although the gas velocity reaches a maximum and becomed choked, the mass flow rate is not choked. The mass flow rate can still be increased if the source pressure is increased. ]
Whenever the ratio of the absolute source pressure to the absolute downstream ambient pressure is less than [ ( k + 1 ) / 2 ]^{ k / ( k  1 )}, then the gas velocity is nonchoked (i.e., subsonic) and the equation for the mass flow rate is:
or this equivalent form:
where: ^{ } _{ }^{ } _{ } _{ } ^{ } ^{ } _{ }^{} 
Q C A^{ } g_{c}^{ } k_{ }_{ } ρ^{ } P^{ } P_{A}^{ } M R T Z 
= mass flow rate, lb / s = discharge coefficient (dimensionless, usually about 0.72) = discharge hole area, ft^{ 2} = gravitational conversion factor of 32.17 ft / s^{ 2}_{ } = c_{p} / c_{v} of the gas = (specific heat at constant pressure) / (specific heat at constant volume) = real gas density, lb / ft^{ 3} at P and T = absolute source or upstream pressure, lb / ft^{ 2} = absolute ambient or downstream pressure, lb / ft^{ 2}_{ } = gas molecular weight = the Universal Gas Law Constant = 1545.3 ftlb / ( lbmol · °R ) = gas temperature, °R = the gas compressibility factor at P and T (dimensionless) 



where: ^{ }_{ } ^{ } ^{ } ^{ } _{ }^{ } 
Q C A^{ } g_{c}^{ } d^{ } P^{ } P_{A}^{ } H 
= mass flow rate, lb / s = discharge coefficient (dimensionless, usually about 0.62) = discharge hole area, ft^{ 2} = gravitational conversion factor of 32.17 ft / s^{ 2}_{ } = source liquid density, lb / ft^{ 3} = absolute source pressure, lb / ft^{ 2} = absolute ambient pressure, lb / ft^{ 2}_{ } = height of liquid above bottom of discharge opening, ft 



where: ^{ }_{ } ^{ } ^{ } 
Q C A^{ } g_{c}^{ } d^{ } H 
= mass flow rate, lb / s = discharge coefficient (dimensionless, usually about 0.62) = discharge hole area, ft^{ 2} = gravitational conversion factor of 32.17 ft / s^{ 2}_{ } = source liquid density, lb / ft^{ 3} = height of liquid above bottom of discharge opening, ft 
Three different methods of calculating the rate of evaporation from a nonboiling liquid pool are presented in this section.
Method developed by the U.S. Air Force:^{ 2}
The following equations are for predicting the rate at which liquid evaporates from the surface of a pool of liquid which is at or near the ambient temperature. The equations were derived from field tests performed by the U.S. Air Force with pools of liquid hydrazine.

where:^{ } _{ } _{ } _{ } _{ } _{ } 
E^{ } u T_{A} T_{F} T_{P} M P_{S} P_{H} 
= evaporation flux, ( lb / minute ) / ft^{ 2} of pool surface = windspeed just above the liquid surface, miles / hour = ambient temperature, °K_{ } = pool liquid temperature correction factor_{ } = pool liquid temperature, °F_{ } = pool liquid molecular weight = pool liquid vapor pressure at ambient temperature, mm Hg_{ } = hydrazine vapor pressure at ambient temperature, mm Hg_{ } 


Method developed by U.S. EPA:^{ 5, 6}
The following equations are for predicting the rate at which liquid evaporates from the surface of a pool of liquid which is at or near the ambient temperature. The equations were developed by the United States Environmental Protection Agency ( U.S. EPA ).

where: ^{ } ^{ } 
E u M A^{ } P T R^{ } 
= evaporation rate, lb / minute = windspeed just above the pool liquid surface, m / second = molecular weight of the pool liquid = surface area of the pool liquid, ft^{ 2} = vapor pressure of the pool liquid at the pool temperature, mm Hg = pool liquid temperature, °K = the Universal Gas Law constant = 82.05 ( atm · cm^{ 3} ) / ( gmol · °K ) 

Method developed by Stiver and Mackay:^{ 3}
The following equations are for predicting the rate at which liquid evaporates from the surface of a pool of liquid which is at or near the ambient temperature. The equations were developed by Warren Stiver and Dennis Mackay of the Chemical Engineering Department at the University of Toronto.

where:^{ } _{ } ^{ } 
E^{ } k T_{A} M P R^{ } u 
= evaporation flux, ( lb / s ) / ft^{ 2} of pool surface = mass transfer coefficient, ft / s = ambient temperature, °R _{ } = pool liquid molecular weight = pool liquid vapor pressure at ambient temperature, mm Hg = the Universal Gas Law constant = 555 ( mm Hg · ft^{ 3} ) / ( lbmol · °R ) = windspeed just above the liquid surface, miles / hour 
The following equation is for predicting the rate at which liquid evaporates from the surface of a pool of cold liquid (i.e., liquid temperature of about zero degrees Centigrade or less).

where: ^{ } 
E^{ } B M e 
= evaporation flux, ( lb / minute) / ft^{ 2} of pool surface = atmospheric boiling point of pool liquid, °F = molecular weight of pool liquid = 2.7183 ( the number that is the base of the natural logarithm system ) 

where: ^{ } _{ } _{ } 
Q D P^{ } T T_{B} c_{p} 
= initial instantaneous mass flow, lb / s = discharge hole diameter, in = absolute source pressure, lb / in^{ 2} = source liquid temperature, °R = atmospheric boiling point of source liquid, °R_{ } = source liquid specific heat, Btu / lb / °F_{ } 
(1) _{ } (2) _{ } 
Calculate the singlephase flow component ( Q_{S }) for the source liquid by using the same equation as for a liquid discharge from a pressurized source, except substitute the source pressure minus the source liquid vapor pressure for the source pressure. Calculate the flashing flow component ( Q_{F }) by using the same equation as for a flashing saturated liquid. 

where: 
Q_{Total} 
= initial instantaneous mass flow, lb / s 

where: _{ }^{ } _{ }^{ } _{ }^{ } 
X H_{s}^{L} H_{a}^{V} H_{a}^{L} 
= weight percent vaporized = source liquid enthalpy at source temperature and pressure, Btu / lb_{ } ^{ } = flashed vapor enthalpy at atmospheric boiling point and pressure, Btu / lb_{ } ^{ } = residual liquid enthalpy at atmospheric boiling point and pressure, Btu / lb_{ } ^{ } 

where: _{ } _{ } _{ } 
X c_{p} T_{s} T_{b} H 
= weight percent vaporized = source liquid specific heat, Btu / lb / °F _{ } = source liquid temperature, °F _{ } = source liquid atmospheric boiling point, °F _{ } = source liquid heat of vaporization at atmospheric boiling point, Btu / lb 
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