quesiton about sample problem (PE exam) 2

[karussel]

Hi all,

I'm studying for the upcoming controls PE exam and am having problems with a sample question that I suspect has the wrong answer in the answer key:

Given a basic gas flow control valve loop where conditions are as follows:

Inlet P: 80psia
Outlet P: 30psia
Op. Temp: 140F
Mole weight of the gas: 40

If only the upstream gas (P inlet) increased by 10 psi, which of the following best describes how the mass flow would change?

A) F outlet = 1.062 * F inlet
B) F outlet = 1.095 * F inlet
C) F outlet = 1.125 * F inlet
D) F outlet = 1.162 * F inlet

I believe the answer should be A - due to the relationship between P inlet and Q (flow) - which would be the square root of the increase percentage - i.e. sq root of 1.125 = 1.0607

The answer key says C, which implies a linear relationship between the flow increase and the inlet pressure increase. Either it's a typo, or am I just missing something? The only thing I can figure is that there is something attributed to gas density change due to the pressure increase, but I cant put my finger on it.

Thanks for any help you can offer with this; I'm new to valving (background is in manufacturing - PLC's robotics, instrumentation - but NO valve experience) and didn't expect the controls exam to include so much emphasis on valve mechanics and theory.

 

[zdas04]

Let me run through the thought process that I would use on this problem:

- With that dP flow is choked.
- "Choked flow" says that velocity is 1.0 Mach (which is a function of gas composition and temperature, independent of pressure).
- Volume flow rate is velocity times flow area, so the volume flow rate (at actual conditions) is constant.
- Mass flow rate is the product of actual volume flow rate and flowing density.
- Flowing density is the ratio of Pressure over temperature times a gas-specific constant, so a 12.5% increase in pressure would be a 12.5% increase in density which would be a 12.5% increase in mass flow rate.

So, if the answer were "C. Mass flow rate after change = Initial mass flow rate * 1.125" then it is right. If it is saying that the flow downstream of the choke is 1.125 times flow upstream of the choke then it is ludicrous because of the continuity equation.

David

 

[ione]

Take a look at this FAQ

http://www.eng-tips.com/faqs.cfm?fid=1198

You are in choked conditions (as already noted). Increasing upstream pressure (or reducing upstream temperature) produces an increase of density and consequently an increase of mass flow rate. More specifically being the mass flow rate proportional to the upstream pressure you'll have:

Q2/Q1 = P2/P1 = 1.125 (and the winner is "C")

 

[zdas04]

ione,
Your "or reducing upstream temperature" statement has a problem. If I lower upstream temperature then I'll reduce velocity by the square root of the temperature change (in absolute terms, so if you lower the upstream temperature from 140F to 130F you'll lower sonic velocity by 0.8%). This means that if the problem was a change in temperature instead of pressure you'd need to recalculate both volume flow rate (at actual conditions) and density to get the new mass flow rate.

David

 

[ione]

David,

Your post was definitely opportune and precise. I just wanted to emphasize that in a choked flow a change in upstream conditions, which leads to a change in density, implies a change in mass flow rate.
Being the absolute upstream temperature at denominator in the mass flow rate equation, a reduction of temperature leads to a mass flow rate increase.