Critical flow conditions

A critical flow condition corresponds to AL = 0, and the final pressure corresponds to choked pressure. 

For critical flow conditions (i.e., when total superimposed plus built-up back 

Under critical flow conditions, only the upstream conditions pi, t)i, and Ti need be known to determine flow rate, which, for P < 0.2, is 

Therefore critical flow conditions exist and the fluid velocity in the choke is sonic. 

Note that critical flow conditions apply, since relieving pressure of 97.2 psia is over twice the backpressure of 14.7 psia. 

For steam flow under critical flow conditions, the following equation is obtained by substituting the appropriate constants in Equation (4)  

In the above equation, is the critical velocity (m/s), K is the ratio of specific heats (Cp/C ) at inlet conditions, P is the pressure in the restriction at critical flow conditions (KPa, absolute - Note that this term is known as the critical flow pressure ), and p, is the density of the fluid at the critical flow temperature and pressure (kg/m ). 

Note In practice, these coordinates should be checked against the flow conditions of the chosen dimensions of the Parshall flume. If the flumes are shown to be submerged forcing them not to be at critical flows, other coordinates of the parabolic cross sections must be tried until the flumes show critical flow conditions or unsubmerged. 

The following equations are used for sizing control valves for gas and steam conditions. These equations apply to both subcritical and critical flow conditions [10]. 

In PR valve design, it is desirable to select a PR valve discharge location at a low enough pressure to permit designing for critical flow conditions, so that the relieving rate will be independent of minor back pressure fluctuations. 

In the above relation Eq. (7.11) served to calculate the emission velocity hj and he are the enthalpies for the initial state and for critical flow conditions, respectively, and V = Vn,/M. 

Line sizes based on velocity limitations are calculated only in special cases where corrosion, erosion or deposits on the pipe wall have to be accounted for or where critical flow conditions exist. 

A common prerequisite to the application of all these equations is the evaluation whether the ratio of set pressure of the relief device to the counterpressure is high enough to ensure critical flow conditions in the vent area. 

The flow coefficient C is determined by calibration with water, and it is not entirely satisfactory for predicting the flow rate of compressible fluids under choked flow conditions. This has to do with the fact that different valves exhibit different pressure recovery characteristics with gases and hence will choke at different pressure ratios, which is not significant for liquid flows. For this reason, another flow coefficient, C, is often determined by calibration with air under critical flow conditions (Fisher Controls, 1977). The corresponding flow equation for gas flow is 

This equation is cubic in liquid depth. Below a minimum value of E, there are no real positive roots above the minimum value there are two positive real roots. At this minimum value of E, the flow is critical that is, Fr = 1, V= V , and E, = (3/2)h. Near critical flow conditions, wave motion and sudden depth changes called hydraulic jiunps are likely. Chow Open Channel Hydraulics, McGraw-Hill, New York, 1959) discusses the numerous surface profile shapes which may exist in nonuniform open channel flows. 

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