flow of gas through needle

[knowlittle]

I need to estimate nitrogen flow through a 19 gauge needle (0,027" internal dia). The needle is 3" long. Upstream pressure is 30 psi, downstream 0 (open to air). How much is coming out? Room temperature. Thanks.

 

[racookpe1978]

So, what have YOU calculated so far?

What equations have YOU looked up so far?
What results have YOU gotten so far, and why do you feel you need your work second-checked by others? That is, why do you think you might have made an error in YOUR calculations?

What Reynolds number are YOU using?
What coefficients for the nitrogen gas are YOU assigning at the inlet, mid-point and exit? (pressure, density, etc) at the three points?

 

[BigInch]

What racookpe is politely telling you is that this is "Engineering Tips", not "Engineering Free".

 

[georgeverghese]

We'll give you a few hints

Supply pressure = P1 = 45psia
Pressure at end of needle = P2
Pressure at exit of needle = P3 = 14.51psia

Assume a flow Q1.

Step 1 : Compute pressure P2 ( flow through 3inches of smooth flow straight tube with id = 0.027inch) based on compressible flow behaviour for flow of Q1
Step 2: Flow through needle exit will be critical flow - with pressure P2 from step 1 exiting into atmosphere, compute Q2 for given nozzle exit dia.

When results are converged, Q1 assumed = Q2 computed

For flow being critical at the needle exit, you could use Cd = 0.8.