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This page calculates the head loss coefficient and head loss at a smooth bellmouth pipe entrance.

The head loss h_L can be calculated as:

h_L = k_loss x (u_m² / (2 x g) )

Where k_loss is the head loss coefficient, u_m is the mean flow velocity in the pipe, and g is the gravitational acceleration. k_loss is calculated from:

k_loss = 235.03x⁴ - 194.09x³ + 56.739x² - 7.8163x + 0.50

Where x is the defined as:

x = r / D_h

Where r is the radius of the pipe and D_h is the hydraulic diameter.

The k_loss equation was derived from a curve fit from points when plotted from the following data and are accurate plus/minus 10%:

r/Dh	kloss
0.00	0.5
0.01	0.44
0.02	0.37
0.03	0.31
0.04	0.26
0.05	0.22
0.06	0.2
0.08	0.15
0.10	0.12
0.12	0.09
0.16	0.06
0.20	0.03

References

Roberson, John A. and Crowe, Clayton T., Engineering Fluid Mechanics, 2nd Ed., Rudolf Steiner Press, London.1976. p 360 - 384.

Idel'chik, I E. and Fried, Erwin., Flow Resistance, a Design Guide for Engineers, Taylor & Francis, Washington D.C. 1989. p 52.

ASHRAE. ASHRAE Handbook, 1977 Fundamentals, American Society of Heating, Refrigerating And Air Conditioning Engineers, Inc., New York, 1997. p 32.31.