# Gas Flow Rate Calculation using Pressure Drop

1. Feb 13, 2014

### mallorn

1. The problem statement, all variables and given/known data
Hi everyone,

I'm trying to calculate the flow rate of air in straight tubing that is 30cm long and has a diameter of .1875 in and has an outlet into a 100 mL vial which is vented to the atmosphere. The starting of the system pressure is 20 psi and the ending psi is 14.6, since it's in equilibrium with the atmosphere. The end goal of the problem is to see how long it takes to completely flush the vial with air three times. To do that, I'd need the volumetric flow rate of the air in the tubing.

2. Relevant equations and 3. The attempt at a solution

I was using the flow rate calculator from pipeflowcalculations.com but got a result (.002 cubic meters/sec, which is 120,000 mL/min) that I wanted to confirm using manual calculations.

However, I've been running into some problems that I wanted to consult with you guys:

I was thinking to calculate it using the Darcy-Weisenbach equation V=sqrt(2g*Pressure Drop/density* (length/diameter)*darcy friction factor. Would it be ok to ignore the friction factor in this case since the length is so small?

Another option would be to use the definition of pressure as density*head*gravity and the equation as follows:

V= Square root (2*g*h)
Pressure/g*density= h

But when I try to solve it the units don't match up, even when I convert them all to SI.

What do you all think is the best approach and is my train of thought correct? Thank you very much!

2. Feb 13, 2014

### SteamKing

Staff Emeritus
I can't comment on your calculation unless you show them, units and all.

Looking at a flow rate of 0.002 cu.m./s and a tubing diameter of 3/16", the velocity of the air flowing in the tube is approximately M = 0.32, which is the threshhold of where compressibility effects start to become significant.

However, given that the vial is flushed about 1200 times over, I think you're safe, although I can't figure out why this is a matter of such importance.

3. Nov 4, 2014

4. Nov 4, 2014

### Staff: Mentor

Does 2000 liters/sec really sound reasonable to you for this system?

Chet

5. Nov 4, 2014

### SteamKing

Staff Emeritus
Not sure where 2000 L/s comes from. OP was talking about 0.002 m3/s, which I believe is 2 L/s.

6. Nov 4, 2014

### Staff: Mentor

Oops. My mistake.
Chet

7. Nov 4, 2014

### Staff: Mentor

I checked to see whether, at 2 L/s, one predicts a pressure drop of ~5 psi in this tube. I get a Reynolds number of about 50000 for this flow, so it's in the turbulent region. Assume that the temperature remains about constant. For this Reynolds number, the friction factor is about 0.005. This leads to a wall shear stress of 0.0074 psi, and a pressure drop of about 2 psi in the tube. This is on the order of the 5 psi pressure drop in the problem description. So the results are probably about right, give or take.

Chet