Reference: Pipe Flow – A Practical and Comprehensive Guide, 2012, Publisher Wiley, Donald C. Rennels, Hobart M. Hudson, Chapter 13, Page 142


Pipe Flow Expert File: Case_52_Water_Round_Edged_Orifice_Straight_Pipe.pfe


Problem Description: 

A straight pipe contains a round-edged single-hole orifice. Find the k0 loss coefficient for the orifice with a rounding radius specified as a ratio against the diameter of the orifice (r/d0).


Diagram??Description automatically generated


Use different orifice diameter to pipe diameter ratios ( = d0/d), with varying degrees of rounding to compare the calculated loss coefficient (k0).


The published data uses different calculation methods for comparison: 

Donald C. Rennels, Hobart M. Hudson Equation, Equation 13.6, ASME Fluid Meters, and Alvi et al.


A screen shot of a computer??Description automatically generated


Pipe Flow Expert Parameters:


Fluid Data: Water at, 68 °F

Pipe Data: Internal Diameter 4 inches, wall thickness 0.237 inches, roughness 1881 micro-inches


The following 45 systems with an inflow demand of 0.4 ft3/sec were used to model orifices with orifice / pipe diameter ratios ( = d0/d1) from 0.1 through to 0.9.

System #

r/do (Rounding Radius / Orifice Diameter)

1 – 9

1.00

10 – 18

0.25

19 – 27

0.18

28 – 36

0.125

37 – 45  

0.08


Result Comparison: 


Pipe Flow Expert Calculated Results and Published Graph Readings of Orifice Loss Coefficient (k0):


Orifice Diameter / Pipe Diameter (d0/d1)

Rounding Radius / Orifice Diameter (r/d0)

Donald C. Rennels, Hobart M. Hudson (k0)

ASME Fluid Meters

Low  Flow Nozzle (k0)

ASME Fluid Meters

High  Flow Nozzle (k0)

Alvi et al.

(k0)

Pipe Flow Expert

(k0)

0.1

1.0

1.01

-

-

-

1.01

0.2

1.0

0.95

0.95

-

-

0.95

0.3

1.0

0.85

0.86

-

-

0.85

0.4

1.0

0.72

0.74

-

-

0.72

0.45

1.0

-

-

0.68

-

-

0.5

1.0

0.58

0.61

-

-

0.58

0.6

1.0

0.42

-

0.47

-

0.42

0.7

1.0

0.27

-

0.33

-

0.27

0.8

1.0

0.13

-

0.19

-

0.13

0.9

1.0

0.04

-

-

-

0.04

0.1

0.25

1.32

-

-

-

1.32

0.2

0.25

1.25

-

-

1.255

1.25

0.3

0.25

1.14

-

-

-

1.14

0.4

0.25

0.99

-

-

1.06

0.99

0.5

0.25

0.81

-

-

-

0.81

0.6

0.25

0.62

-

-

0.625

0.62

0.7

0.25

0.41

-

-

-

0.41

0.8

0.25

0.22

-

-

0.28

0.22

0.9

0.25

0.07

-

-

-

0.07

0.1

0.18

1.48

-

-

-

1.48

0.2

0.18

1.41

-

-

1.37

1.41

0.3

0.18

1.29

-

-

-

1.29

0.4

0.18

1.12

-

-

1.12

1.12

0.5

0.18

0.93

-

-

-

0.93

0.6

0.18

0.71

-

-

0.695

0.71

0.7

0.18

0.48

-

-

-

0.48

0.8

0.18

0.26

-

-

0.31

0.26

0.9

0.18

0.09

-

-

-

0.09

0.1

0.125

1.67

-

-

-

1.67

0.2

0.125

1.59

-

-

1.57

1.59

0.3

0.125

1.45

-

-

-

1.45

0.4

0.125

1.28

-

-

1.275

1.28

0.5

0.125

1.06

-

-

-

1.06

0.6

0.125

0.82

-

-

.79

0.82

0.7

0.125

0.56

-

-

-

0.56

0.8

0.125

0.31

-

-

-

0.31

0.9

0.125

0.10

-

-

-

0.10

0.1

0.08

1.88

-

-

-

1.88

0.2

0.08

1.79

-

-

1.795

1.79

0.3

0.08

1.65

-

-

-

1.65

0.4

0.08

1.46

-

-

1.465

1.46

0.5

0.08

1.22

-

-

-

1.22

0.6

0.08

0.95

-

-

-

0.95

0.7

0.08

0.66

-

-

-

0.66

0.8

0.08

0.37

-

-

-

0.37

0.9

0.08

0.12

-

-

-

0.12


Graphical Comparison of Results: 

Chart??Description automatically generated


Commentary: 

The published k0 loss coefficients compare well with the calculated results.


Note:        Head Loss in m fluid = (k0 * v2) / 2g 

  • where v = fluid velocity in m/s at the entrance to the orifice, g = acceleration due to gravity in m/s2
  • k0 is not the same as a standard k value (which is used in formulas where v = velocity in the pipe)