I'd like to convert CFM to ft/min

[sciguyjim]

I'd like to be able to convert a volume CFM value to a linear speed of feet/min. The flow = 575 CFM and the pipe diam is 3". This calculation looks correct, do you agree?

pipe area=7.065 in^2
575 CFM = 993600 cubic inches/min
length of tube to hold 993600 cu in = 993600 in^3/7.065 in^2 = 140636.94 inches or 11719.7 ft.
so, linear speed is 11,719.7 feet/min or 133.2 mph

Reynold's number = [rho*V*D]/u
rho = density of air at 40°F = 1.127 kg/m^3
Velocity = 133.2 mph = 59.5 meters/sec
Diam = 3" = 0.0762 meters
Dynamic Viscosity of air = u = 1.87x10^-5 N*s/m^2

Re=273,246 which is in the transitional region between laminar and turbulent flow, right?

 

[TD2K]

Close, but you sure make make things hard.

A comment first, 3" pipe does not have an ID of 3" which is the back calculated ID from 7.065 in2 area. Sch 40 is the most common and has an ID of 3.068" which gives you an internal area of flow of 7.393 in2. (sch 80 has an ID of 2.900 in2).

Secondly, since you have the flow in ft3/min (I'm assuming these are actual ft3/min, not at standard conditions), if you simply divide the volumetric flow rate by the area, you get the velocity. If you think about it, the velocity of the fluid times the area it flows through gives you the volumetric flow rate.

From an equation point of view and calculation (except for the diameter for 3" pipe), the Re number is right. Didn't check the individual data.

A pipe with an area of 1 m2 area with the fluid flowing at 10 m/sec must be flowing at 10 m3/sec volumetric flow rate.

 

[sciguyjim]

TD2K,
"Close, but you sure make make things hard."

Yes I do. I seem to have my own brand of math logic. In school teachers used to wonder how I could be so good in science yet so bad in math when you need the math to do the science. Thanks for making it easier for me. This is only the second time in the last 26 years that I'm doing fluid flow calcs like this so I don't exactly have a good grasp of what's going on.

 

[TD2K]

Hey, if it works for you and you can keep track of it, do what makes sense to you.

I'd be the last person to say any calculation has to be done in one set method. Your method seemed long to me but it's correct and as I said, if it works for you, who cares.

 

[TD2K]

BTW, 273,000 for Re is well in the turbulent flow regime, the transition from laminar to turbulent is back in the 2000 Re range.

 

[sciguyjim]

TD2K,
Thanks for the correction about Re value. I've seen more than one value given for the transition region (I thought) and I didn't know which to believe.

 

[TD2K]

The transistion range is not a fixed number but depends on the system and fluid, I've seen numbers from 2000 to 4000 used. However, at 2.7e5, you'll definitely be in turbulent flow.

 

[sciguyjim]

I suspected something like that but I wasn't sure. I went through my library book trying to find the figures I saw but couldn't find them.
I can assume that the airflow everywhere in the narrow pipes is turbulent, not just near the walls or protrusions, etc., right? I feel like I'm gradually getting better able to visualize just what's happening in there.