I need two simple formulas to figure flow rate and velocity of air through an orifice

[intuit]

I have been searching for formulas to determine the flow rate and velocity of air through an orifice at a given pressure differential. I need to know the flow rate to determine the CFM requirements of the compressor. And I need to determine the velocity to be able to accurately size the orifice for the job intended. I have found different formulas. Some more elegant than others. I need simple formulas to get a usable numbers. The application can be fine tuned by trial and error. The variables used should be as follows:

V = Velocity in feet/sec
C = Orifice Coefficient = .95
P = Pressure differential = 130psi (150psi being released into 30psi)
A = Orifice area in inches squared = The orifice sizes will be in the range of .055" to .157" Diameter.
T = Air temperature = 70 degrees F.

I don't need an elegant formula, but if other variables are needed, use:
W = Mass of Air = Assuming .075 lbs/ft
Atmospheric Pressure will not be a factor in this application

 

[RocketSci5KN]

Check this website - they have formula's for what you want. Contact them
if you have any other questions. http://okcc.com/

 

[intuit]

Thank you Rocket. There is some very useful information on that website. However, their formulas are only useful with the charts that they have for their own products. I'm still searching for a formula from which I can create a spreadsheet calculator where I can enter in the pressure and the orifice area. I know that flow and velocity through the orifice (before expansion)are functions of differential pressure, orifice coefficient, and orifice area. But I have no idea what the relationships of all the factors are.

 

[Gannet]

try this online calculator. It requires java

http://www.flowmeterdirectory.com/flowmeter_orifice_calc.html"

 

[alphy]

I would like to clarify that there is not one simple formula that can accurately determine the flow rate and velocity of air through an orifice. This is because there are various factors that can affect the flow rate and velocity, such as the shape and size of the orifice, the properties of the fluid (in this case, air), and the pressure and temperature conditions.

However, there are some commonly used formulas that can provide an estimate of the flow rate and velocity, given the variables provided. One such formula is the Bernoulli's equation, which states that the flow rate is directly proportional to the square root of the pressure differential and the orifice area, and inversely proportional to the square root of the density of the fluid. This can be expressed as:

Q = C * A * √(2ΔP/ρ)

Where:
Q = Flow rate
C = Orifice coefficient
A = Orifice area
ΔP = Pressure differential
ρ = Density of air (can be calculated using the ideal gas law)

Using the given variables, this formula can be simplified to:

Q = 0.95 * A * √(2 * 130/0.075)

Another commonly used formula is the Torricelli's equation, which states that the velocity of a fluid exiting a small orifice is equal to the square root of twice the pressure differential divided by the density of the fluid. This can be expressed as:

V = √(2 * ΔP/ρ)

Using the given variables, this formula can be simplified to:

V = √(2 * 130/0.075)

However, it is important to note that these formulas are only estimates and may not accurately reflect the actual flow rate and velocity. They also do not take into account the shape and size of the orifice, which can significantly affect the flow rate and velocity.

In order to accurately determine the flow rate and velocity, it is recommended to conduct experimental tests using the actual orifice and conditions. This will provide more accurate and reliable results for your specific application.