How to Calculate Air Flow Through a 1/4 Inch Pipe at 90 PSI?

[Norm Koster]

I would like to know the equation for calculating the flow of air through an opening.
I have a 1/4 inch pipe with an area of .0490625 in squared. How much air ( in cu inches) will flow through in 10 seconds if i have 90 psi on one side and atmosphic on the other (14.7 psi).
Thanks

 

[SteamKing]

It's going to depend on the temperature of the air and how long a pipe through which you are flowing the air.

 

[boneh3ad]

Where was this pressure measured? Was it in some large reservoir of a tank feeding the pipe? Is that pressure constant or is the system losing pressure as it vents? You will also need temperature. It's easier if both the temperature and pressure are in a reservoir of some sort so that they are the total temperature and pressure, though you can figure it out regardless. The length of your pipe COULD be a factor if it is long or bendy but would likely be a small error otherwise.

 

[colliflour]

Hagen-Poiseuille equation:
Q=Pi*R^4*deltaP/(8*mu*L)
where Q=volumetric flow rate, R=pipe radius, deltaP=pressure difference, mu=viscosity of air(dependent on temperature as SteamKing said), L=pipe length

A quick calculation at 25 degrees C gave me 4406106 cubic feet per minute with L=1 inch. so just divide 4406106 by the length of the pipe in inches and you'll get the flow rate in a laminar flow regime.

^this equation works for laminar flow only. Actual flow will be significantly higher due to turbulence. For this you would calculate the Reynolds Number and then use an empirical correlation to estimate the flow rate.

 

[cjl]

Hagen-Poiseuille equation:
Q=Pi*R^4*deltaP/(8*mu*L)
where Q=volumetric flow rate, R=pipe radius, deltaP=pressure difference, mu=viscosity of air(dependent on temperature as SteamKing said), L=pipe length

A quick calculation at 25 degrees C gave me 4406106 cubic feet per minute with L=1 inch. so just divide 4406106 by the length of the pipe in inches and you'll get the flow rate in a laminar flow regime.

^this equation works for laminar flow only. Actual flow will be significantly higher due to turbulence. For this you would calculate the Reynolds Number and then use an empirical correlation to estimate the flow rate.

That assumes incompressibility though, which is a much bigger source of error than the laminar flow assumption. In this case, compressibility is key, which will cause the flow to choke at the exit of the pipe (and likely cause a much smaller flow rate than what you just estimated).

 

[colliflour]

http://www.pipeflowcalculations.com/airflow/
Try this. I got flow rates of 149 cfm for 1 inch long pipe for one method and 227 cfm for another method. Depends how in particular the empirical modeling for turbulent flow is done. It also depends on how slippery the inside of the pipe is. Also compared to laminar flow, turbulent flow has much less drop off of flow rate with pipe length. Something like 25% drop in flow with increasing pipe length from 1 inch to 100 inches.

 

[cjl]

http://www.pipeflowcalculations.com/airflow/
Try this. I got flow rates of 149 cfm for 1 inch long pipe for one method and 227 cfm for another method. Depends how in particular the empirical modeling for turbulent flow is done. It also depends on how slippery the inside of the pipe is. Also compared to laminar flow, turbulent flow has much less drop off of flow rate with pipe length. Something like 25% drop in flow with increasing pipe length from 1 inch to 100 inches.

Turbulence won't be the main issue though - compressibility will. The slower drop off of flow rate with pipe length in that calculator is probably because (assuming it is calculating compressibility correctly) the flow is choked at the exit, reducing the influence of upstream factors on flow rate.