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# Nitrogen flow through orifice

## Nitrogen flow through orifice

(OP)
I'm trying to calculate the flow of nitrogen through an orifice and wanted to check to see if my method is correct. The inlet of the orifice is at 1.38 Barg and the outlet is unrestricted flow to atmospheric conditions at 21 C. The cross sectional area of the pipe is 1.78x10^-5 m^2. I have been using Crane 410 equation 2-24, q=Y*C*A*(2*delta_p/rho)^0.5. Here's what I got:

rho=349p'Sg/T=349*2.39*0.967/(21+273)=2.746
d1/d2=0.2
Crane said that for orifices discharging compressible fluids to atmosphere, use the flow coefficient C in the Reynolds number range where C is constant for the given diameter ratio. To me this seemed like the Re>10000 range and C=0.6 in the page A-20 chart.
Pressure ratio delta_p/p'1=1.38/(1.38+1.013)=0.577, so I found the expansion factor Y to be 0.84 with the chart on A-21
q=0.84*0.6*1.78*10^-5*(2*1.38/2.746)^0.5=8.99x10^-6 m^3/s

One strange thing that I noticed was that when I calculated the Re I got a value in the laminar range rather than something in the range I close C from.
Re=d*v*rho/mu=4.7625*(8.99x10^-6/1.78x10^-5)*2.746/0.018=367

Does this seem correct or should I be doing this differently?

### RE: Nitrogen flow through orifice

Take a look at FAQ378-1864: What does the flow profile look like for a Pipeline Blowdown?.

I'm not even going to try to decipher an engineering equation without units. That is such a bad practice that anyone who spends time fighting through the mess is giving your work a false sense of worth and encouraging you to continue with a practice that will create more errors in your work over the years than any other single thing.

I'm guessing that your density is in kg/m3, but even those units, the number you list it is about twice what I'd expect at 1.38 barg (since we don't know your elevation, it is impossible to tell what pressure you used in that equation, I sure hope it wasn't 1.38 or 138 kPa, both of those numbers would be a really big problem for that equation, which is a big enough problem all by itself).

Is your cubic meters per second number at actual conditions or standard? The whole thing is just a mess.

Hint: as long as upstream pressure is above about 0.6 barg the flow out the orifice will be at sonic velocity. Not possible to have sonic laminar flow.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Nitrogen flow through orifice

redeng50,

In thread798-426632: Calculating N2 flow to equipment, you said you have Crane TP410. In the chapter of examples, orifice calculations are covered.

In my experience, laminar gas flow is rare in a plant. Re-check your calcs.

Look for an on-line orifice calculator. Sometimes you can find one that displays intermediate results, which are good for verifying your calcs. Don't just use the on-line calculator though.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Nitrogen flow through orifice

(OP)
Thank you for your replies! I am still in undergrad and have a lot to learn and appreciate the constructive criticism.

Here are the variables for equation 2-24:
q- rate of flow at flowing conditions in m^3/s
Y- net expansion factor for compressible flow through orifices, nozzles, or pipe. This value was found in a table as described in the initial post. No units
C- flow coefficient for orifices and nozzles. Found in a table as described in the initial post.
A- cross sectional area in meters squared
p- pressure in bars gauge
Rho- weight density of fluid, kg/m^3
p'- pressure in bars atmospheric
T- temperature in kelvin
Sg- specific gravity with relation to air. Taken from a table.

We are just above sea level, so to get p' for the rho equation I did 1.013+1.38=2.39 bara at the inlet of the orifice.

Latexman,

I was looking at the examples and they did not have one with this equation. I think it would probably be smart to just use the examples for orifice flow that they have listed as I am not familiar with this equation. I was also able to pull a very similar calculation from work.

Would an online calculator for air flow through an orifice yield similar results to nitrogen? I've been have difficulty finding one specifically for nitrogen.

### RE: Nitrogen flow through orifice

#### Quote (redeng50)

Would an online calculator for air flow through an orifice yield similar results to nitrogen?
Yes, MW=29 vs MW=28.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Nitrogen flow through orifice

Agreed, check units for:
delta_p : should be kpa or Pa for SI
Viscosity : Should be Pa sec, and not cP for SI ( 1cP = 1.0e-3Pa sec)

### RE: Nitrogen flow through orifice

Interesting article for your use. Check your formulas with the results from this table, after converting the units:

I design aqueducts in a parallel universe.

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