Pressure Loss Coefficient for Flow Through Orifice at 45 Degrees

[sovietjet]

Hi. I am looking for a relation or coefficient which describes the pressure loss of a flow through an orifice. Now I know what this is for a normal flat plate orifice for water. What I need is the appropriate coefficients for an orifice plate at an angle both for water(incompressible) and air(compressible). Assuming choked flow at the orifice for the air. Here's a diagram of what I'm talking about.

As you can see the flow approaches the orifices like that. The thin plates are at an angle of 45 degrees. After it passes through, both streams mix. I need to figure out the pressure difference before and after the orifices. I have broken it down into the following.

K = K1 + K2 + K3


K1 = K loss coefficient for a flow through an orifice. I know this already.
K2 = K loss coefficient of the projected area. Since it is at 45 degree the "projected" area is smaller than the actual area of the orifice. In other words what the flow "sees" as it approaches is a smaller hole than what is in fact there. There must be some type of coefficient for this.
K3 = K loss coefficient for the turbulent mixing that occurs after the flow passes through. Any links? Estimates?

Once I get this total K I can get an estimate for the pressure drop. Again, I only need estimates. I know that K1 is about 0.63 for a typical sharp edged orifice. The orifices are circles. The two upstream conditions are:

1) water, incompressible at some flow rate(not low Reynolds number)
2) Air, flow at orifice is choked.

Any ideas?
Thanks

 

[eljose79]

Hello,

Thank you for your post. The pressure loss through an orifice can be described by the discharge coefficient, which is a dimensionless value that relates the actual flow rate through the orifice to the theoretical flow rate (based on the orifice size and fluid properties). This coefficient takes into account the effects of the orifice shape, size, and angle, as well as the fluid properties.

For a flat plate orifice, the discharge coefficient can be calculated using the following equation:

Cd = 0.61 + 0.35(1 - d/D)^4

Where:
Cd = discharge coefficient
d = orifice diameter
D = pipe diameter

However, for an angled orifice, the discharge coefficient will be different and will depend on the angle of the orifice. There are various empirical equations that can be used to calculate the discharge coefficient for angled orifices, such as the following:

Cd = 0.6 + 0.24θ
Where:
θ = orifice angle (in radians)

For the turbulent mixing that occurs after the flow passes through the orifice, there is no specific coefficient that can be used. It will depend on various factors such as the Reynolds number, the geometry of the orifice, and the fluid properties. However, there are empirical correlations that can be used to estimate the pressure loss due to turbulent mixing, such as the Darcy-Weisbach equation:

ΔP = fLV^2/2D

Where:
ΔP = pressure loss
f = friction factor
L = length of the orifice
V = velocity of the fluid
D = diameter of the orifice

In conclusion, to estimate the pressure loss through an angled orifice, you will need to calculate the discharge coefficient using the appropriate equation for angled orifices, and then use the Darcy-Weisbach equation to estimate the pressure loss due to turbulent mixing. I would recommend doing some further research and consulting with other experts in the field for more accurate estimates. I hope this helps. Good luck with your research!