Valve sizing coefficients

CvKvflow coefficientvalve sizingK factorequivalent length

Cv, Kv, K factors and equivalent length — the four coefficients that turn a valve or fitting into a pressure drop at a given flow.

Valve Flow Coefficient (Cv)

Q = C_v \sqrt{\frac{\Delta P}{SG}}

The US valve-sizing relation: Cv is the gpm of 60 °F water a valve passes at 1 psi drop, so Q is in gpm and ΔP in psi.

Valve Flow Coefficient (Kv, metric)

Q = K_v \sqrt{\frac{\Delta p}{SG}}

The metric valve-sizing relation: Kv is the m³/h of water a valve passes at 1 bar drop, related to Cv by Cv ≈ 1.156 Kv.

Minor Loss from K Factor

h_L = K \, \frac{v^{2}}{2g}

Head lost through a valve or fitting as a multiple of velocity head, with g = 9.80665 m/s² and K taken from a fitting table.

Equivalent Length of a Fitting

L_{eq} = \frac{K D}{f}

Converts a fitting's K factor into the length of straight pipe that would cause the same friction loss at the same friction factor.

How they fit together

Cv is defined by an experiment, not a theory: it is the US gallons per minute of 60 °F water that pass the valve wide open with 1 psi across it. Kv is the metric twin — cubic metres per hour at 1 bar — and Cv ≈ 1.156 × Kv. K factors and equivalent lengths describe the same restriction from the pipe side, K as a multiple of velocity head and equivalent length as the feet of straight pipe that would lose as much.

Use Cv or Kv when a manufacturer gives you one, which is always for control and balancing valves; use K or equivalent length for elbows, tees and anything with no catalogue number. Two traps on control valves specifically. Sizing on full design flow at wide open gives a valve that does all its controlling in the first 10% of travel and hunts for the rest — you want the valve to take a real share of the loop's pressure drop, commonly a quarter to a half of it, so it has authority. And Cv assumes cold water: for another fluid divide flow by the square root of specific gravity, and for steam or gas the liquid Cv equation does not apply at all once flow chokes at roughly half the inlet absolute pressure.