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I have a trouble with a simple question (I think). Well, if a have a tank full of compressible air at a pressure of for example 6 bar and a valve with a hole of 8 mm diameter, how can I know the volumetric flow coming out of the valve in function of the actual pressure? The temperature of the ambient is 20 °C and a pressure of 1 bar. I had been searching the way to resolve it but I'm confuse because all the problems I find about compressible air are about turbines and others with not straight out pipe. Thanks for your responses.

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  • $\begingroup$ Not a simple question. Search "The flow of air through circular orifices with rounded approach" $\endgroup$ – pentane Nov 2 '16 at 21:25
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I'm not sure about compressible liquids like air, but you might try Bernoulli's equation. At least, that's what you would use i.e. for water.

For this case: $$ \frac{v^2}{2}=\frac{p}{\rho(p)} $$ Where $\rho$ is dependent on the pressure. I figured something around 380 meters per second, but at such high speeds, friction might play a non-neglectable role.

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If the pressure ratio between high and low pressure is greater than 2 for a compressible fluid such as air, in general the flow is "choked", and exits the valve or orifice at Mach 1 (e.g., 330 m/s). If you know the cross-sectional area of the exit hole, you can calculate a volumetric flow rate, or you can use the ideal gas law at 1 bar to calculate a mass flow rate.

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