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Head Loss at Pipe Entrance Equations and Calculator

Fluids Flow Engineering
Hydraulic & Pneumatic Design Engineering

Head Loss at Pipe Entrance Equations and Calculator using the head loss coefficient and head loss of a fluid at a smooth bellmouth pipe entrance.

 

The head loss h_Lcan 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 = radius in Meters (m)
D_h = Inside diameter in Meters (m)
u_m = Flow Velocity m/s
h_L = Head Loss (m)
k_loss = Head Loss - dimension less
D_h = Diameter Ratio - dimension less

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	k loss
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.