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# Calculating hydrogen gas discharge flow from a pipe opening

## Calculating hydrogen gas discharge flow from a pipe opening

(OP)
I trying to find a quick way to calculate the actual flow rate of hydrogen gas at the discharge point of a 1/8" (0.3175cm) pipe, if the pressure drop is from 74.7psi (515Pa) to 14.7psi (101.4Pa ambient air pressure).  The compressed hydrogen gas is at normal room temperature.

### RE: Calculating hydrogen gas discharge flow from a pipe opening

How long is the tube?  If you want a quick absolute maximum limit, assume energy conservation (Bernoulli) and convert all the pressure to velocity.

Matt

### RE: Calculating hydrogen gas discharge flow from a pipe opening

(OP)
The pipe is 10cm long. I am not sure what you mean with converting all the pressure to velocity.

### RE: Calculating hydrogen gas discharge flow from a pipe opening

Base on critical velocity (which you don't want to pass)
The max flow is ~3lb/hr
BTW most of the pressure drop is probably at your valve.

### RE: Calculating hydrogen gas discharge flow from a pipe opening

(OP)
What equation or reference did you use? 3 lbs of hydrogen gas (H2) occupies a volume of about 15,000L. One Mole of H2 = 2g, which will occupy 22.4 liters as stp. One pound = 0.453592kg
Doesn't temperature AND pressure play a role if you go from a compresed gas @ 60 psi (gauge) to atmospheric pressure?

### RE: Calculating hydrogen gas discharge flow from a pipe opening

Assuming choked flow at your valve the mass flow rate will be a function of the upstream pressure only (you said the upstream temp is room temp).

### RE: Calculating hydrogen gas discharge flow from a pipe opening

(OP)
Which function or reference would you use to calculate the mass flow rate at constant pressure but different orifice sizes?

### RE: Calculating hydrogen gas discharge flow from a pipe opening

Choked flow

M=C*A*{k*ρ*P(2/k+1)^[(k+1)/(k-1)]}^0.5

K(H2)=1.410

Minimum P/Pd  required for H2 choked flow = 1.899

M= mass flow rate, kg/s
C = discharge coefficient, dimensionless (~0.62)
A = discharge hole cross-sectional area, m²
k = cp/cv of the gas
cp = specific heat of the gas at constant pressure
cv = specific heat of the gas at constant volume
ρ = real gas density at P and T, kg/m³
P = absolute upstream pressure of the gas, Pa
Pd = absolute downstream gas pressure

good luck

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