2-K (Hooper’s) method

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.

New Crane Method

The latest version of the equivalent length method given in Crane Technical Paper 410 (Crane Co. 1991) requires the use of two friction factors. The first is the actual friction factor for flow in the straight pipe (f ), and the second is a standard friction factor for the particular fitting(fT)

hL = Kfv²_/2g

where

Kf = 4f(Leq/D)

The value of f is determined from the Colebrook equation

f =0.0625/[log(3.7D/E)]²

where

E is the pipe roughness (0.0018 in., 0.045mm) for commercial steel pipe.

The Crane paper gives fT for a wide variety of fittings, valves, etc. This method gives satisfactory results for high turbulence levels (e.g., high Reynolds number) but is

less accurate at low Reynolds number. This method provides a better estimate for the effect of geometry, but does not reflect any Reynolds number dependence.