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Critical Pressure Drop Across Valve for Compressible Flow

Critical Pressure Drop Across Valve for Compressible Flow

Critical Pressure Drop Across Valve for Compressible Flow

(OP)
I'm working on a valve sizing problem and have encountered some valve equations and measurements that I do not understand.

In Flow Equations for Sizing Control Valves ISA-75.01.01-2007 (pdf), equation 14b (Page 17) provides the flow coefficient for turbulent, choked flow to be: C = Q/(0.667N7P1)*SQRT[(GgT1Z)/(FyXT)]

The term of interest is xT, which is the critical pressure drop ratio at which the valve is choked. xT = (P0 - P)/P0

I understand that for air, the critical ratio across an orifice is P/P0 = 0.53, which corresponds to an xT of 0.47. However, the document linked above (Table 2, page 26) provides some example measurements for valves and shows xT to vary from 0.2 to 0.84 (suggesting critical pressure ratios P/P0 of 0.8 to 0.14).

I can understand how internal frictional losses might reduce the critical pressure ratio (thus increasing xT), but I cannot find a reason why the critical pressure ratio could be any higher than 0.53 (xT would be any lower than 0.47).

Can someone help me understand these critical pressure ratios in valves?

RE: Critical Pressure Drop Across Valve for Compressible Flow

The simplified formula for the critical press ratio is what is in common use. The full expression for this ratio shows that it is also a function of the beta ratio. Take a look at equation 10-24 and 10-25 in Perry 7th edition.

RE: Critical Pressure Drop Across Valve for Compressible Flow

xT is a function of the control valve only, "pressure differential ratio factor of a control valve without attached fittings at choked flow". Where in the PDF did you find the equation xT = (P0 - P)/P0? I see x >= FγxT (and x >= FγxTP) @ choked flow. These are conditional statements to determine which equations and pressures to use.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

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