Reference: Pipe Flow – A Practical and Comprehensive Guide, 2012, Publisher Wiley, Donald C. Rennels, Hobart M. Hudson, Chapter 13, Page 145


Pipe Flow Expert File: Case_56_Water_5deg_Bevel_Edged_Orifice_Straight_Pipe.pfe


Problem Description: 

A straight pipe contains a 45o bevel-edged single-hole orifice. The orifice diameter to pipe diameter is specified by the ratio d0/d1. The orifice thickness to orifice diameter is specified by the ratio t/d0.


Diagram, schematic??Description automatically generated


Use different orifice thickness to orifice diameter ratios (t/d0) to compare the loss coefficient (k0) through the orifice with varying orifice diameter to pipe diameter ratios (d0/d).


Calendar??Description automatically generated


Pipe Flow Expert Parameters:


Fluid Data: Water at, 68 °F


One hundred and forty-three individual systems with inflow demands of 0.01 ft3/sec were used to model a range of bevel thickness to orifice diameter ratios (t/d0) across a range of orifice diameter to pipe diameter ratios (d0/d).


Result Comparison: 


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


Orifice Diameter / Pipe Diameter (d0/d)

Orifice Thickness / Pipe Diameter (t/d0)

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

Pipe Flow Expert

(k0)

0.1

1.0

1.94

1.9400

0.2

1.0

1.85

1.8514

0.3

1.0

1.71

1.7065

0.4

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.5

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.6

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.7

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.8

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.9

1.0

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.5

2.04

2.0367

0.2

0.5

1.95

1.9457

0.3

0.5

1.79

1.7910

0.4

0.5

1.59

1.5949

0.5

0.5

1.34

1.3439

0.6

0.5

Bevel Limit Exceeded

Bevel Limit Exceeded

0.7

0.5

Bevel Limit Exceeded

Bevel Limit Exceeded

0.8

0.5

Bevel Limit Exceeded

Bevel Limit Exceeded

0.9

0.5

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.3

2.13

2.1256

0.2

0.3

2.03

2.0323

0.3

0.3

1.88

1.8800

0.4

0.3

1.67

1.6723

0.5

0.3

1.41

1.4135

0.6

0.3

1.11

1.1144

0.7

0.3

Bevel Limit Exceeded

Bevel Limit Exceeded

0.8

0.3

Bevel Limit Exceeded

Bevel Limit Exceeded

0.9

0.3

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.2

2.20

2.2004

0.2

0.2

2.11

2.1053

0.3

0.2

1.95

1.9497

0.4

0.2

1.74

1.7372

0.5

0.2

1.47

1.4717

0.6

0.2

1.16

1.1635

0.7

0.2

0.80

0.7983

0.8

0.2

Bevel Limit Exceeded

Bevel Limit Exceeded

0.9

0.2

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.15

2.25

2.2535

0.2

0.15

2.16

2.1570

0.3

0.15

2.00

1.9992

0.4

0.15

1.78

1.7832

0.5

0.15

1.51

1.5129

0.6

0.15

1.20

1.1982

0.7

0.15

0.82

0.8240

0.8

0.15

Bevel Limit Exceeded

Bevel Limit Exceeded

0.9

0.15

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.1

2.33

2.3261

0.2

0.1

2.23

2.2278

0.3

0.1

2.07

2.0667

0.4

0.1

1.85

1.8461

0.5

0.1

1.57

1.5690

0.6

0.1

1.25

1.2455

0.7

0.1

0.86

0.8590

0.8

0.1

0.50

0.4978

0.9

0.1

Bevel Limited Exceeded

Bevel Limit Exceeded

0.1

0.07

2.39

2.3862

0.2

0.07

2.29

2.2863

0.3

0.07

2.12

2.1225

0.4

0.07

1.90

1.8980

0.5

0.07

1.62

1.6154

0.6

0.07

1.29

1.2850

0.7

0.07

0.89

0.8878

0.8

0.07

0.52

0.5156

0.9

0.07

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.05

2.44

2.4385

0.2

0.05

2.34

2.3372

0.3

0.05

2.17

2.1712

0.4

0.05

1.94

1.9432

0.5

0.05

1.66

1.6559

0.6

0.05

1.32

1.3185

0.7

0.05

0.91

0.9129

0.8

0.05

0.53

0.5310

0.9

0.05

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.03

2.51

2.5087

0.2

0.03

2.41

2.4056

0.3

0.03

2.24

2.2365

0.4

0.03

2.00

2.0039

0.5

0.03

1.71

1.7101

0.6

0.03

1.36

1.3641

0.7

0.03

0.95

0.9465

0.8

0.03

0.55

0.5517

0.9

0.03

Bevel Limit Exceeded

Bevel Limit Exceeded

0.1

0.02

2.56

2.5563

0.2

0.02

2.45

2.4520

0.3

0.02

2.28

2.2808

0.4

0.02

2.05

2.0451

0.5

0.02

1.75

1.7469

0.6

0.02

1.40

1.3951

0.7

0.02

0.97

0.9693

0.8

0.02

0.57

0.5657

0.9

0.02

0.19

0.1896

0.1

0.01

2.62

2.6216

0.2

0.01

2.52

2.5157

0.3

0.01

2.34

2.3416

0.4

0.01

2.10

2.1016

0.5

0.01

1.80

1.7975

0.6

0.01

1.44

1.4376

0.7

0.01

1.00

1.0006

0.8

0.01

0.59

0.5850

0.9

0.01

0.20

0.1962

0.1

0.005

2.67

2.6694

0.2

0.005

2.56

2.5623

0.3

0.005

2.39

2.3861

0.4

0.005

2.14

2.1430

0.5

0.005

1.83

1.8345

0.6

0.005

1.47

1.4687

0.7

0.005

1.02

1.0236

0.8

0.005

0.60

0.5990

0.9

0.005

0.20

0.2011

0.1

0.001

2.73

2.7329

0.2

0.001

2.62

2.6241

0.3

0.001

2.45

2.4452

0.4

0.001

2.20

2.1980

0.5

0.001

1.88

1.8837

0.6

0.001

1.51

1.5102

0.7

0.001

1.05

1.0541

0.8

0.001

0.62

0.6178

0.9

0.001

0.21

0.2076


Graphical Comparison of Formula: 

Chart??Description automatically generated


Commentary: 

The published loss coefficients compare well with the calculated results.


Bevel Limit: There is a point where beveling is limited by the available radial distance between the pipe wall and the face of the orifice. The dashed red line on the above graph plots the bevel limit cut off point across each t/do line. Points below the dashed red line are not valid and should not be calculated. 

The Pipe Flow Expert software reports a ‘Bevel Limit Exceeded’ message for any defined orifice data that is in this region. 


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)