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.)
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.