Compressed Air - Bernoulli Equation

[fonz]

I'm trying to ascertain the dynamics of a compressed air system in terms of flow rate, air consumption, pressure drop etc.

To keep it simple my system consists of a 5.5 bar supply (550000Pa) supply on 12mm OD Nylon Tubing and is reduced to 6mm OD Nylon through a valve (pressure drop assumed neglible for now) so the valve is treated as a simple orifice.

So I'm trying to work out the flow through the 6mm OD section (at 1 bar to start) after the valve opens. Then i want to work out how long it takes to fill up my 10m section of pipe (and actuator it is driving). If pressure drop is going to be an issue then i'd like to allow for it but i don't know how.

Also, in my calculations I used a simplified version of Bernoulli's principle. This I am told only applies to incompressible fluids or gases moving at velocities low than the speed of sound. So how valid are my calculations and do I have to alter them?

And no i don't have a copy of Crane's TP 410

I have attached a PDF copy of my calc i did in Mathcad, if you can spot any errors please let me know.

Regards
Dan

 

[fonz]

Basically all i need to know is if my actual flow rate i calculated - 0.03m³/s (1800litres/min) is going to change by more than 50 litres/min if i account for flow turbulance/friction/pressure drop etc. I don't need to crunch some serious numbers, just roughly.