The Darby 3K method provides a way to calculate a fitting's loss coefficient (K) over a wide range of Reynolds numbers and fitting sizes. It is similar in purpose to the Hooper 2K method but introduces an additional coefficient to provide a more flexible representation of the effect of fitting diameter.

 

K1 – Low-Reynolds-Number Constant: controls the Reynolds-number-dependent component of the fitting loss. The term K1/Re becomes increasingly important as Reynolds number decreases and therefore accounts for the increased K-value associated with laminar and low-Reynolds-number flow.


Ki – Turbulent-Flow Base Constant: defines the base value of the fitting's loss coefficient in the high-Reynolds-number region. It can be regarded as the limiting turbulent-flow K-value for a fitting of very large diameter.


Kd – Diameter Correction Constant: controls the effect of fitting size on the turbulent-flow loss coefficient. Together with Ki, it determines the fully turbulent K-value for a fitting of a particular diameter.  


The K value is calculated (for use on the upstream pipe) from the fitting’s K constants in conjunction with the size of the fitting and the fluid’s Reynolds Number:



Where: 

Kf = K value fitting loss coefficient (for use with velocity on the upstream pipe).

K1 = The laminar-flow constant for the fitting.

NRe = The Reynolds number.

Ki = The fully turbulent loss coefficient for the fitting.

Kd = The diameter constants for the fitting.

Dn = The nominal pipe diameter in inches.


Equation as defined in Darby, R., "Chemical Engineering Fluid Mechanics," 3rd Edition, 2017