Reference: Pipe Flow – A Practical and Comprehensive Guide, 2012, Publisher Wiley, Donald C. Rennels, Hobart M. Hudson, Chapter 13, Page 140


Pipe Flow Expert File: Case_51_Water_Sharp_Edged_Orifice_Straight_Pipe.pfe


Problem Description:

A straight pipe contains a sharp-edged single-hole orifice. 


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Use different diameter ratios ( = d0/d) to calculate the loss coefficient (k0) of the orifice, where d0 is orifice diameter and d is the pipe diameter.


The published data uses different calculation methods: 

Rennels / Hudson, Equation 13.3, ASME Fluid Meters, and Alvi et al.


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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


Nine systems, each with an inflow demand of 0.4 ft3/sec, were used to model orifice diameter to pipe diameter ratios ( = d0/d) from 0.1 through to 0.9.


Result Comparison: 


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


Orifice Diameter / Pipe Diameter (d0/d)

ASME Fluid Meters

(High k0)

ASME Fluid Meters

(Low k0)

Alvi et al.

(k0)

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

Pipe Flow Expert

(k0)

0.1

-

-

-

2.77

2.77

0.2

2.67

2.54

-

2.67

2.67

0.205

-

-

2.64

-


0.3

2.48

2.44

-

2.49

2.49

0.4

2.21

2.17

2.23

2.24

2.24

0.5

1.9

1.79

-

1.92

1.92

0.6

1.52

1.45

-

1.53

1.53

0.61

-

-

1.44



0.7

1.13

1

-

1.09

1.09

0.8

0.749

0.59

-

0.63

0.63

0.815

-

-

0.55



0.9

0.21

0.21

-

0.22

0.22


Graphical Comparison of Results: 

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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)