Related Resources: heat transfer
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_{L}can be calculated as:
h_{L}= k_{loss} x (u_{m}^{2} / (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} = 235.03x^{4}  194.09x^{3} + 56.739x^{2}  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 / D_{h}

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.