# Mass Flow Rate Through PSV

1. Nov 5, 2009

### 0507476h

Hi all,

I am designing a pressure relief system for a high pressured gas (air) system. System consists of a highly pressurised gas receiver with PSV mounted driectly on it which vents via tailpipes to atmosphere.

I know the max mass flow rate out of the container
I know the back pressure accumulated by the piping etc downstream of the valve, therefore I know the differential pressure across the valve

How do I calculate the mass flow rate out of the valve?

2. Nov 5, 2009

### minger

Theoretically you can use Bernoulli's equation to calculate a velocity, and therefore a mass flow. However, there will be frictional losses through the valve; you may need to consult with the manufacturer to obtain some sort of friction factor.

Also, if the velocity and Mach number are high enough, you may need to consider compressibility factors.

3. Nov 5, 2009

### FredGarvin

You should also consult the ASME specs in which they spell out how to size pressure reliefs for pressure piping systems, which relates to the BPV code.

4. Nov 5, 2009

### Q_Goest

Hi minger,
That's actually a very good answer. ASME BPV Code regulates the RV industry to a large degree. They certify relief valves and also provide equations to determine relief capacity. Any company that manufactures relief valves and wants to have them stamped must meet the same basic kind of regulations that pressure vessel manufacturers must meet. That is to say, relief valve manufacturers are audited by the national board just as vessel manufacturers are. And RV manufacturers have to test the performance of their valves under ASME code conditions, just as vessel manufacturers must test their vessels under ASME code conditions.

ASME Section VIII, Div 1, provides requirements for both RV certification and sizing valves. Not sure if Div 1 provides ALL the requirements for certification, but it provides all the requirements for calculating flow. They're provided in mandatory appendix 11. The equations are based on Bernoulli's equation and other factors that are taken into consideration such as compressibility factors, two phase flow, etc...

Also, there is something called a coefficient of discharge, which is basically the same as what minger is referring to as a "friction factor". The relief valve manufacturer can provide this since it's a value that is certified by test.

For air, the equation is:
Wa = CKAP(M/T)^.5

where
Wa = flow (lbm/hr)
C = 356
K = Coefficient of discharge as provided by valve mfg.
A = area of RV orifice (in2) as provided by valve mfg.
P = Pressure (psia) that is 10% higher than relief device set pressure (ex: if RV set pressure is 100 psig, P = (100 *1.1) + 14.7 = 124.7 psia)
M = molecular weight = 28.97
T = absolute temperature (R)

Last edited: Nov 6, 2009
5. Nov 6, 2009

### stewartcs

Just to add to what everyone else has said...

API RP520 (Part I) has a lot of good information as well for PRV's.

I would also note that the mass flow rate will differ depending on whether the flow is critical or sub-critical. Q_Goest's equation is for critical flow, however I would also consider the compressibility factor (since it is gas relief) and even an additional K_b capacity correction factor for back pressure (this is in addition to the discharge coefficient).

Typically I would check to see if the flow is critical or sub-critical first, then use the appropriate equation based on that. If the pressure downstream of the nozzle is less than or equal to the critical flow pressure, then critical flow will occur. If the downstream pressure exceeds the critical flow pressure, then sub-critical flow will occur.

Just my 2 cents...

CS