Sonic pressure drop

Figure 4-13 Sonic pressure drop for adiabatic pipe flow for various heat capacity ratios. From AICHE/CCPS, Guidelines for Consequence Analysis of Chemical Releases (New York American Institute of Chemical Engineers, 1999).

Table 4-4 Correlations1 for the Expansion Factor Yg, and the Sonic Pressure Drop Ratio (P1 - P2)/Pi, as a Function of the Excess Head Loss K,2...

The equation used to fit the expansion factor and the sonic pressure drop ratio is of the form... 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

Sudden vapor condensation in the pool may cause water hammer if the holes are too big and the pressure drop is too low Sonic hole velocity is desirable to avoid this problem. 

Sonic hole velocity is desirable in smaller holes and is essential in V2.- to 2-in holes. A minimum sparger pressure drop of 10 psi shoiild be used. 

If pressure drop is high enough to exceed the critical ratio, sonic velocity will be reached. When K = 1.4, ratio = 0.53. 

Eor good control, design the pressure drop for the control valve between the fractionating system and the jet system for sonic velocity (approximately 2 1 pressure ratio). This means that the jets suction must be designed for half the absolute pressure of the evacuated system. 

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows ... 

Since the pressure drop is quite high, there is a possibility of approaching sonic velocity in the line. This will result in a potential noise problem. Hence, it is a good practice to limit the velocity to 60 percent of the sonic velocity or a 0.6 Mach number. 

When the relieving scenarios are defined, assume line sizes, and calculate pressure drop from the vent tip back to each relief valve to assure that the back-pressure is less than or equal to allowable for each scenario. The velocities in the relief piping should be limited to 500 ft/sec, on the high pressure system and 200 ft/sec on the low pressure system. Avoid sonic flow in the relief header because small calculation errors can lead to large pressure drop errors. Velocity at the vent or flare outlet should be between 500 ft/sec and MACH 1 to ensure good dispersion. Sonic velocity is acceptable at the vent tip and may be chosen to impose back-pressure on (he vent scrubber. 

There are two flow regimes corresponding to sonic (or choked) flow for liigher pressure drops and subsonic flow for lower pressure drops. The transition between the two flow regimes occurs at tlie dimensionless critical pressure ratio, Ter,I, which is related to tlie gas lieiit capacity ratio y via... 

Sonic velocity will be established at a restricted point in the pipe, or at the outlet, if the pressure drop is great enough to establish the required velocity. Once the sonic velocity has been reached, the pressure drop in the system will not increase, as the velocity will remain at this value even though the fluid may be discharging into a vessel at a lower pressure than that existing at the point where sonic velocity is established. 

In general, the sonic or critical velocity is attained for an outlet or downstream pressure equal to or less than one half the upstream or inlet absolute pressure condition of a system. The discharge through an orifice or nozzle is usually a limiting condition for the flow through the end of a pipe. The usual pressure drop equations do not hold at the sonic velocity, as in an orifice. Conditions or systems exhausting to atmosphere (or vacuum) from medium to high pressures should be examined for critical flow, otherwise the calculated pressure drop may be in error. 

If sonic velocity of step 2 is greater than calculated velocity of step 1, calculate line pressure drop using usual flow equations. If these velocities are equal, then the pressure drop calculated will be the maximum for the line, using usual flow equations. If sonic velocity is less than the velocity of step 1, reassume line size and repeat calculations. 

If the pressure drop across the valve is to be more than 42 per cent of the inlet absolute pressure the valve selection is the same as if the pressure drop were only 42 per cent. With this pressure ratio the steam flow through the valve reaches a critical limit, with the steam flowing at sonic velocity, and lowering the downstream pressure below 58 per cent of the inlet absolute pressure gives no increase in flow rate. When the heater needs a higher pressure, or when the pressure required in the heater is not known, it is safer to allow a smaller pressure drop across the control valve. If the necessary heater pressure is not known, a pressure drop across the control valve of 10-25 per cent of the absolute inlet pressure usually ensures sufficient pressure within the heater. Of course, in the case of pressure-reducing valves the downstream pressure will be specified. 

If the outlet or discharge pressure is lowered further, the pressure upstream at the origin wtill not detect it because the pressure wave can only travel at sonic velocity. Therefore, the change in pressure downstream will not be detected upstream. The excess pressure drop obtained by lowering the outlet pressure after the maximum discharge has been reached takes place beyond the end of the pipe [3]. This pressure is lost in shock waves and turbulence of the jetting fluid. See References 12,13, 24, and 15 for further expansion of shock waves and detonation waves through compressible fluids. 

Six-tenths factor, 47 Yearly cost indices, 47 Critical flow, safety-relief, 438 Back pressure, 440 Sonic flow, 438 Critical flow, see Sonic Cyclone separators, 259-269 Design, 260-265 Efficiency chart, 263 Hydroclones, 265-267 Pressure drop, 263, 264 Scrubber, 269 Webre design, 265 Deflagration venting nomographs,... 

The design of the network calls for the selection of pipe diameters such that the discharge through each valve attains the maximum (sonic) velocity for an initial transitory period. Since the flare pressure and the process unit pressures are specified, this requirement amounts to the stipulation of a maximum allowable pressure drop over each path Sj (labeled with a roman numeral) from the valve to the flare. The optimal design in this case may be formulated as the following constrained minimization problem ... 

In isentropic flow (just as in isothermal flow), the mass velocity reaches a maximum when the downstream pressure drops to the point where the velocity becomes sonic at the end of the pipe (e.g., the flow is choked). This can be shown by differentiating Eq. (9-25) with respect to P2 (as before) or, alternatively, as follows... 

The ratio of the sonic velocity in a homogeneous two-phase mixture to that in a gas alone is cm/c = Pg/ePm = Vpl/ATO — ). This ratio can be much smaller than unity, so choking can occur in a two-phase mixture at a significantly higher downstream pressure than for single phase gas flow (i.e., at a lower pressure drop and a correspondingly lower mass flux). 

The next step in the procedure is to determine the sonic pressure ratio. This is found from Equation 4-64. If the actual ratio is greater than the ratio from Equation 4-64, then the flow is sonic or choked and the pressure drop predicted by Equation 4-64 is used to continue the calculation. If less than the ratio from Equation 4-64, then the flow is not sonic and the actual pressure drop ratio is used. 

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