Critical Flow Behavior
If a compressible gas is expanded across a nozzle, an orifice, or the end of a pipe, its velocity and specific volume increase with decreasing downstream pressure. For a given set of upstream conditions (using the example of a nozzle), the mass rate of flow through the nozzle will increase until a limiting velocity is reached in the throat. It can be shown that the limiting velocity is the velocity of sound in the flowing media at that location. The flow rate that corresponds to the limiting velocity is known as the critical flow rate.
The absolute pressure ratio of the pressure in the throat at sonic velocity (๐๐๐) to inlet pressure (๐1) is called critical pressure ratio.(๐๐๐) is known as the critical flow pressure.ย ย Under critical flow conditions, the actual pressure in the throat cannot fall below the critical flow pressure even if a much lower pressure exists downstream. At critical flow, the expansion from throat pressure to downstream pressure takes place irreversibly with energy dissipated in turbulence into the surrounding fluid.ย
The critical flow pressure ratio in absolute units may be estimated using the ideal gas relationship in the equation below.
The value of the coefficientย Cย can be evaluated from the expression of the ratio of the specific heats of the gas or vapor.ย The ratio of specific heats of any ideal gas and possibly the ratio of specific heats of a diatomic actual gas can be found in any acceptable reference work.ย When k cannot be determined, it is suggested thatย Cย = 315
When the ratio of back pressure to inlet pressure exceeds the critical pressure ratioย (๐๐๐–ย ๐1)ย the flow through the pressure relief valve is subcritical. This equation may be used to calculate the required effective discharge area for a conventional relief valve that has its spring setting adjusted to compensate for superimposed back pressure and for sizing a pilot-operated relief valve.
The value of the coefficient C can be evaluated from the expression of the ratio of the specific heats of the gas or vapor.ย ย The ratio of specific heats of any ideal gas and possibly the ratio of specific heats of a diatomic actual gas can be found in any acceptable reference work.ย ย When k cannot be determined, it is suggested that C = 315