COEFFICIENT OF VELOCITY C v and K v Equations for Gases Machinery's Handbook, 31st Edition
2761
for Non-choked Turbulent Flow when x < F g x T
SG p i T i Z ∆ p -----------
SG p i T i Z ∆ p -----------
Q 1360 p i Y ----------
Q 482 p i Y ---------
=
=
C v
K v
for Choked Turbulent Flow when x ≥ F g x T
SG p i T i Z F γ ∆ p -----------
SG p i T i Z F γ ∆ p -----------
Q 907 p i -------
Q 321.5 p i ---------
=
=
C v
K v
for Laminar or Transitional Flow
MT i ∆ p p i p o + ( ) --------------
MT i ∆ p p i p o + ( ) --------------
Q N 1 F R -------
Q N 2 F R -------
=
=
C v
K v
N 1 = 1730 for T s = 0 ° C N 1 = 1840 for T s = 15 ° C N 2 = 4920 for T s = 0 ° C N 2 = 5200 for T s = 15 ° C The following definitions apply to equations for C v and K v given above: Q = flow in gpm for liquids, and flow in SCFM for gasses SG = specific gravity D p = p i - p o is the pressure differential between upstream and downstream, p i is inlet absolute pressure (psia or bar), and p o is outlet absolute pressure (psia or bar) F F = liquid critical pressure ratio factor (ranges between 0.68 to 0.96) F L = liquid pressure recovery factor. F L depends on valve geometry and ranges between 0.6 for ball valves and 0.9 for globe valves P v = absolute vapor pressure of the liquid at inlet temperature x = ∆ p p i ---- is the ratio of the pressure differential to the inlet absolute pressure F g = specific heat ratio factor. F g = 1 for air, otherwise F γ γ 1.4 = ---- x T = choked flow pressure differential ratio factor, experimentally determined, that varies from 0.3 to 0.9 depending on valve geometry Y = expansion factor for gases. Y 1 x 3 F γ x T = – -------- for normal flow, and ranges from Y = 1 to Y = 0.667 at choked flow Z = compressibility factor (assume Z = 1 for ideal gasses) F R = Reynolds number factor that depends on valve characteristics, and is limited to F R ≤ 1 M = molecular mass of fluid in kg/kg-mol or lb/lb-mol T i = absolute inlet temperature for the gas, ° C T s = absolute reference temperature for the gas, ° C For additional information on flow equations see International Electrotechnical Com mission standard IEC 60534.
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