K is a dimensionless factor defined as the excess head
loss in pipe fitting, expressed in velocity heads. K does not depend on the roughness
of the fitting (or the attached pipe) or the size of the system, but it is a
function of the Reynolds number and the exact geometry of the fitting. The 2-K method
accounts for these dependencies by the following equation.

Kf= K1/Re + Koo(1 + 1/IDin.)

Or in SI units

Kf= K1/Re + Koo(1 + 25.4/IDmm.)

where

K1 = K for the fitting at Re = 1

Koo = K for a large fitting at Re= infinity

ID = Internal pipe diameter, in. (mm).

The ID correction in the two K expression accounts for
the size differences. K is higher for small sizes, but nearly constant for
larger sizes. However, the effect of pipe size (e.g., 1/ID) does not accurately
reflect data over a wide range of sizes for valves and fittings. Further

Hooper’s scaling factor is not consistent with the Crane
values at high Reynolds numbers and is especially inconsistent for larger fitting
sizes.