Frictional Losses through Fittings and Valves: These losses are reported as resistance coefficient K, where K is the number of the velocity heads that is lost because of the fittings or an obstruction. These values are independent of friction factor. Fitting friction loss h_ff is given as

And sum of form friction loss and skin friction loss is designated as friction loss h_f given as

Bernoulli equation for incompressible fluid is:

which can be written as

The equivalent length of a fitting or an obstruction is the length of the pipe that offers the same pressure drop due to friction. It is usually expressed in terms of the equivalent pipe diameters L_e/d.

There are minor losses that include contraction, entrance, enlargement and exit losses. Sudden contraction loss coefficient for turbulent flow conditions is given as a function of β² where β is the ratio of d₂ to d₁.

β²	0	0.2	0.4	0.6	0.8
K_c	0.5	0.45	0.36	0.21	0.07

The frictional loss for a sudden enlargement with turbulent flow, is given by Borda-Carnot Equation as

where V₁ is the velocity in smaller duct. The expansion loss coefficient, K_e, is shown as follows

β²	0	0.2	0.4	0.6	0.8
K_e	1.0	0.64	0.36	0.16	0.04

Modules:

gate_p Fully open 3/4 open 1/2 open 1/4 open

L_p		(Pipe length, ft)
d		(Pipe diameter, inch)
ε		(Pipe roughness, ft)
K		(Fitting Losses, no of velocity heads)
n_gate		(Number of gate valves)
n_globe		(Number of globe valves)
n_check		(Number of check valves)
n_90		(Number of 90 deg std. elbows)
n_45		(Number of 45 deg std. elbows)
V		(Velocity, ft per sec)
ρ		(Density, lb per ft³)
μ		(Viscosity, cP)
Z1		(Elevation at Point 1, ft)
Z2		(Elevation at Point 2)