Resistance Coefficient K for Sudden Expansion-Contraction

The losses through these fitting are generally evaluated by first obtaining

ß = d2 / d1

Important Note:

the resulting K values as tabled below are based on the flow velocity in the larger pipe,

if the flow velocity in the small pipe is used to evaluate the head loss then the K values tabled below should be multiplied by 

( ß)^4 = (d2 / d1) ^4

Head loss (h):

h_expansion(he) = Ke*(v2)^2 / (2*g)

h_contraction(hc) = Kc*(v2)^2 / (2*g)

v2= Average velocity (m/s) of water in small pipe

g =  Constant of gravity 9.8 m/s^2

Table of Ke & Kc against β = d2 / d1

β	Ke	Kc
0.15	1887.42	965.43
0.2	576	300
0.25	225	120
0.3	102.23	56.17
0.35	51.31	29.24
0.4	27.56	16.41
0.45	15.51	9.72
0.5	9	6
0.55	5.32	3.81
0.6	3.16	2.47
0.65	1.87	1.62
0.7	1.08	1.06
0.75	0.6	0.69
0.8	0.32	0.44
0.85	0.15	0.27
0.9	0.06	0.14
0.95	0.01	0.06
1	0	0

Ref : http://www.roymech.co.uk/Related/Fluids/Fluids_Pipe.html