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Air flow through an orifice (hole) calculator

Empirical correlations for the discharge coefficient are employed to approximate the actual mass flow rate through an orifice. The actual mass flow rate differs from the ideal mass flow rate (discharge of an ideal nozzle) because of the losses associated with the constriction.

– D_h: hole hydraulic diameter
– L: hole length
– p_0,in: hole inlet total (driving) pressure
– p_out: hole outlet pressure
– T_0,in: hole inlet total (driving) pressure

Calculators

Calculators for different correlations are presented below. New calculators will progressively be added.

1) Incompressible non-cavitating flow through long sharp-edged orifices (orifices are also called nozzles) [4]

Limit conditions below:

• Length must be smaller than 10 times the diameter (L/D_h < 10)
• Outlet pressure must be smaller than inlet total pressure (p_0,in > p_out)

Enter length of the hole (L): mmminch

Enter hydraulic diameter (D_h): mmminch

Enter inlet total pressure (p_0,in): PaMPabarlbf/in^{2 (psi)}

Enter outlet pressure (p_out): PaMPabarlbf/in^{2 (psi)}

Enter inlet total temperature (T_0,in): K°C°F

1) C_d = …

2) m = … kg/s

3) m_iso = … kg/s

Other parameters that determine the value of the discharge coefficient include [1]:
– presence of crossflow at hole inlet and (or) hole outlet
– thickness of the boundary layer near hole inlet and (or) hole outlet
– hole rotation and presence of swirl within the hole
– hole inclination and orientation. The inclination is the angle between the hole axis and and the wall surface. The orientation is the angle between the hole axis and the crossflow. For blade design, inclination and orientation causes changes in discharge coefficient up to 30 % [2,3].
– hole radiusing at inlet and (or) outlet, and the degree of radiussing
– hole chamfering, i.e., if a slope is cut at hole outlet and (or) inlet edge

The change in discharge coefficient that arises from the presence of these parameters can be determined with ad-hoc empirical correlations.

References

[1] Hay N., Lampard D. (1996). Discharge coefficient of turbine cooling holes: a review
[2] Hay N., Lampard D. (1983). Effect of crossflows on the discharge coefficient of film cooling holes.
[3] Byerley, A.R. (1989). Heat transfer near to a film cooling hole in a gas turbine blade.
[4] Lichtarowicz A., Duggins R. K., Markland E. (1965). Discharge Coefficients for Incompressible Non-Cavitating Flow through Long Orifices.