6 replies to this topic

[cTaejin]

Dear All,

I have some (maybe very simple) question about gas flow rate of an orifice.

Let's say the orifice hole diameter is fixed.

When inlet and outlet pressure ratio (p2/p1) is lower than a certain value,
the gas velocity reaches to its speed of sound and is not changed even when the p2 decreases further. (right?)

In this case, the flow rate is dependent on the inlet pressure only (not on pressure differences).

My question is
"How the flow rate can be changed with fixed orifice diameter and fixed gas velocity ?" (Q = V_fixed*A_fixed)

Isn't there any maximum flow rate of an fixed orifice (which is independent on the p1)?

Thanks in advance...

[daryon]

Dear All,

I have some (maybe very simple) question about gas flow rate of an orifice.

Let's say the orifice hole diameter is fixed.

When inlet and outlet pressure ratio (p2/p1) is lower than a certain value,
the gas velocity reaches to its speed of sound and is not changed even when the p2 decreases further. (right?)

In this case, the flow rate is dependent on the inlet pressure only (not on pressure differences).

My question is
"How the flow rate can be changed with fixed orifice diameter and fixed gas velocity ?" (Q = V_fixed*A_fixed)

Isn't there any maximum flow rate of an fixed orifice (which is independent on the p1)?

Thanks in advance...

Hi,

No I don't think so, the flowrate of a compressible fluid through an orifice will never be independant of the upstream pressure P1. It will, like you say be independant of the downstream pressure P2 when sonic velocity is realised. Such that reducing P2 further, given a constant P1 will not increase the flowrate. However increasing the upstream pressure P1 will still increase the flowrate through the orifice. Theorectically, i guess P1 can continue to increase untill sonic velocity is realised somewhere in the upstream piping. However, normally the upstream pressure is fixed by something in the system like a pressure trip or relief valve.

Edited by daryon, 08 September 2009 - 12:44 AM.

[cTaejin]

Thanks for your reply.

But I still don't understand the equation Q = A_fixed * V_fixed, when I assume the orifice flow reach to its speed of sound, V_fixed.

Do you means that orifice flow can be higher than the speed of sound? (larger flow through a fixed hole requres higher speed.. right?)

[daryon]

Thanks for your reply.

But I still don't understand the equation Q = A_fixed * V_fixed, when I assume the orifice flow reach to its speed of sound, V_fixed.

Do you means that orifice flow can be higher than the speed of sound? (larger flow through a fixed hole requres higher speed.. right?)

No, my understanding (i could be wrong)is maximum possible velocity in the orifice is sonic velocity but its not a constant. Q = A_fixed*V_variable. For an ideal gas i think you can take V as constant, but for non-ideal gas mixtures V (the speed of sound) will change with upstream pressure P1.

[fallah]

When inlet and outlet pressure ratio (p2/p1) is lower than a certain value,
the gas velocity reaches to its speed of sound and is not changed even when the p2 decreases further. (right?)

In this case, the flow rate is dependent on the inlet pressure only (not on pressure differences).

My question is
"How the flow rate can be changed with fixed orifice diameter and fixed gas velocity ?" (Q = V_fixed*A_fixed)

Isn't there any maximum flow rate of an fixed orifice (which is independent on the p1)?

Thanks in advance...

Two illustrating points:

Under chocked flow condition the actual pressure at the VC (vena contracta) can not fall below the critical flow pressure,even if a much lower pressure exists downstream.

With increasing upstream pressure,the fluid density increases accordingly.The velocity at VC decreased and more mass is allowed to pass through the RO.Therefore,increase in upstream pressure will increase mass flow passing the RO but velocity at VC still remains at Mach No=1.

Edited by fallah, 10 September 2009 - 06:39 AM.

[shan]

You should not mix the following two concepts
1. flow through orifice
2. flow through piping.

The choke flow rule (when p2/p1 is lower than a certain valve, p2 does not affect flow. ) is for orifice, while Mach number rule (the flow velocity can not excess Mach number) is for piping. For example, choke outlet flow velocity may excess Mach number such as supersonic flare tip and it is still not critical flow if p2/p1 is much lower the critical value in a 100 mile pipeline.

Now let us attack your question. If a section of piping is downstream of the orifice, the maximum flow is fixed because velocity in the piping is not allowed higher than Mach number. However, if no piping is downstream of the orifice, the maximum flow is infinity if p1 is infinity because choke flow does not set limit on the maximum flow.

[JoeWong]

Hi,

No I don't think so, the flowrate of a compressible fluid through an orifice will never be independant of the upstream pressure P1. It will, like you say be independant of the downstream pressure P2 when sonic velocity is realised. Such that reducing P2 further, given a constant P1 will not increase the flowrate. However increasing the upstream pressure P1 will still increase the flowrate through the orifice. Theorectically, i guess P1 can continue to increase untill sonic velocity is realised somewhere in the upstream piping. However, normally the upstream pressure is fixed by something in the system like a pressure trip or relief valve.

cTaejin,
daryon has pointed out that the flowrate of a compressible fluid will never be independent of P1 but will be independent of P2 when choked flow (sonic velocity at vena contrata) occurred. Just wanna to add...

My question is
"How the flow rate can be changed with fixed orifice diameter and fixed gas velocity ?" (Q = V_fixed*A_fixed)

For compressible fluid, mass flow passing through an fixed bore size RO is a function of
i) composition (which affect k, MW, ...)
ii) Differential pressure across RO (P1-P2)
iii) density (again function of P1, MW, z, T1)

If composition and upstream pressure (P1) are fixed,
i) remain unchanged
ii) reducing P2 lead to higher P1-P2 which will result higher mass flow passing RO. Mass flow increase will continue until until P2 reach critical pressure of fluid (Pc). Infact at this moment, sonic velocity (Mach no =1) occurred at vena contrata, some distance downstream of RO. When P2 lower than Pc, further reduction of P2 will not result any mass flow increase.
iii) reduce upstream temperature (T1) will results higher density and higher mass flow passing RO.