High pressure tank discharge rate calculation

[CraigHassler]

I need to calculate the flow rate of air through a 3/4" orifice from the pressurized side of a 1000 PSI (~250 cu ft at pressure) tank to the open atmosphere and know the time it will take to release 20% - 35% - 50% of the volume of the pressure tank.

Tank size ~1.5 cu ft at atmospheric pressure, ~250 cu ft at max working pressure. (approx. 2500 PSI)

Basically I need to know how to calculate the the flow rate of a high pressure tank discharging to the atmosphere by knowing the following:

1. Tank Volume at pressure.
2. Tank pressure.
3. Tank orifice size.
4. Assume a discharge nozzle length of 1" the same size as the orifice.
5. Using an explosive burst disk to initiate the flow (time 300 ns)

The flow calculator at pipeflowcalculations.com/airflow are not doing the trick for me due mostly to my inability to completely understand their use.

[PipeFlowCalcs]

Calculator for gas discharge is under development and will be available soon. But your problem is calling for non-steady flow calculation which is another kind of problem.

Here are results for 1000 psi 3/4" orifice discharge (chocked flow):
1. pressure in position 1 (p1):
p1 : 1000 psi

2. pressure in position 2 (p2):
p2 : 101325.0 Pa - atmospheric pressure

3. pressure drop (p1-p2):
p1-p2 : 6793675 Pa

4. tube diameter (D):
D : 0.75 in

5. volume flow rate (q1):
q1 : 204.95366 m3/h

6. weight flow rate (w):
w : 17096.828 kg/h

7. velocity (V1):
V1 : 199.74394 m/s

8. expansion factor (Y):
Y : 0.606

9. temperature (T1):
T1 : 288 K

10. density (ρ1):
ρ1 : 83.41802 kg/m3

11. gas constant (R):
R : 287 J/kgK

12. K factor - minor losses coefficient (K ):
K : 1.5

Please note that q1 is on p1 and T1. To have it on standard conditions that flow should be converted: q=13947 m3/h; p=101325; T=288K

Mass of air in the tank will change over time as air flows out of the reservoir and on 50% of pressure 50% of mass will be in it (volume is the same).
For 1" pipe 3/4" diameter I get 202 m3/h which is almost the same as without it (q1=205 m3/h).

[CraigHassler]

Thank you very muck for your time and trouble, this information will be very useful.

[pedrosydow]

Hi
My problem is very similar to the previous one. I need to know how internal pressure i need to have in a reservoir of 8 m3, to achieve a discharge mass flow of 45 kg / min instantaneously via an outlet 2.5".

Thanks.

[admin]

You can use gas discharge calculator (now it is finished), but it is for steady flow. As reservoir discharge, pressure will decrease and so will flow rate.

[CraigHassler]

Again thank you for your efforts and continuing to assist me. I now have enough information to scale the tanks I am going to be using.