Critical Pressure Drop Across Valve for Compressible Flow

[calzone]

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[(G_gT₁Z)/(F_yX_T)]

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

I understand that for air, the critical ratio across an orifice is P/P₀ = 0.53, which corresponds to an x_T of 0.47. However, the document linked above (Table 2, page 26) provides some example measurements for valves and shows x_T 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 x_T), but I cannot find a reason why the critical pressure ratio could be any higher than 0.53 (x_T would be any lower than 0.47).

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

 

[georgeverghese]

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.

 

[Latexman]

x_T 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 x_T = (P0 - P)/P0? I see x >= F_γx_T (and x >= F_γx_TP) @ 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.