Reference: Pipe Flow – A Practical and Comprehensive Guide, 2012, Publisher Wiley, Donald C. Rennels, Hobart M. Hudson, Chapter 13, Page 146


Pipe Flow Expert File: Case_53_Water_Thick_Edged_Orifice_Straight_Pipe.pfe


Problem Description: 

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


Chart, box and whisker chart??Description automatically generated


Use different orifice thickness to orifice diameter ratios (t/d0) to compare the calculated orifice loss coefficient (k0) across a range of different orifice diameter to pipe diameter ratios.


The published data uses different calculation methods for comparison: 

Donald C. Rennels, Hobart M. Hudson, Equation 13.13, James A.J., Sanderson E. W.


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 27 systems, each with an inflow demand of 0.4 ft3/sec, were used to model orifices with a 

thickness / diameter ratio (t/d0) ranging from 0.2 through to 2.0.

System #

 = d0/d1 (Orifice Diameter / Pipe Diameter)

1 – 9

0.75

10 – 18

0.50

19 – 27

0.25


Result Comparison: 


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


Orifice Thickness / Orifice Diameter (t/d0)

Orifice Diameter / 

Pipe Diameter 

( = d0/d1)

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

James 
 (k0)

Sanderson ( = 0.252)

(k0)

Pipe Flow Expert

(k0)

0.2

0.75

0.8539

-

-

0.8539

0.4

0.75

0.8093

-

-

0.8093

0.6

0.75

0.7211

-

-

0.7211

0.8

0.75

0.6114

-

-

0.6114

1.0

0.75

0.5243

-

-

0.5243

1.2

0.75

0.4889

-

-

0.4889

1.25

0.75

0.4868

-

-

0.4868

1.3

0.75

0.4860

-

-

0.4860

1.39

0.75

0.4858

-

-

0.4858

2

0.75

0.4858

-

-

0.4858

0.2

0.5

1.8977

-

-

1.8977

0.4

0.5

1.7959

-

-

1.7959

0.6

0.5

1.5947

-

-

1.5947

0.8

0.5

1.3446

-

-

1.3446

1.0

0.5

1.1458

-

-

1.1458

1.2

0.5

1.0652

-

-

1.0652

1.25

0.5

1.0604

-

-

1.0604

1.3

0.5

1.0585

-

-

1.0585

1.39

0.5

1.0581

-

-

1.0581

2

0.5

1.0581

-

-

1.0581

0.132

0.25

-

-

2.52

-

0.2

0.25

2.6000

-

-

2.6000

0.245

0.25

-

-

2.74

-

0.4

0.25

2.5583

-

-

2.5583

0.5

0.25

-

2.5

2.28

-

0.6

0.25

2.4222

-

-

2.4222

0.75

0.25

-

1.87

-

-

0.8

0.25

2.1553

-

-

2.1553

0.995

0.25

-

1.61


-

1.0

0.25

1.8188

-

1.7

1.8188

1.2

0.25

1.5531

-

-

1.5531

1.25

0.25

1.4454

-

-

1.4454

1.3

0.25

1.4389

-

-

1.4389

1.39

0.25

1.4364

-

-

1.4364

1.4

0.25

-

-

1.62

-

1.6

0.25

-

-

1.56

-

1.89

0.25

-

1.55

1.58

-

2

0.25

1.4358

-

-

1.4358


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)