Calculation of laminar / viscous sublayer

[chrisjc]

Hi there,

I'm interested in determining whether or not a pressure pipe can be considered to hydraulically smooth or not however i've only found one unreferenced equation for calculating the laminar sublayer thickness:

http://wiki.answers.com/Q/What_is_meant_by_Hydraulic_smooth_pipe

t=5D*(8^0.5)/((f^0/5)*Re

There are no examples of this equation in my fluids book, on wikipedia, or on engineeringtoolbox, so i'm not happy to blindly plug this equation into my model!

Is this easy enough to calculate this for a particular turbulent flow based on reynolds number and roughness or something?

Thanks for reading

Regards

Chris

 

[btrueblood]

Should be f^(1/5), not 0/5. Would suggest looking up the Moody chart and equations in a good reference text on fluid mechanics. The poster is a bit goofy in saying "Hydraulically smooth mean that the roughness on the wall of the pipe is less than 1/2 of the thickness of the viscous sublayer of the turbulent flow." The transition from rough to smooth pipe is more of a range and educated guessing than some magic line; look at a Moody friction factor chart and you'll see why.

 

[katmar]

I had a brief look at this a while back, but didn't get too far. The approach I took was to use Colebrook-White to calculate the friction factor for a given pipe size and flow rate with a roughness of zero, and then setting some tolerance above this friction factor (I think I used 2%) and calculate by trial and error the roughness that would give this slightly higher friction factor.

You could probably come to some analytical solution by using one of the explicit friction factor equations rather than using Colebrook-White. The results weren't very important to what I was doing, so I did not perservere very far with it.

I think that any attempt at trying to calculate the exact thickness of the boundary sublayers would involve so many assumptions and approximations that you couldn't have much confidence in the answers anyway.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[chrisjc]

Hi thanks guys.

btrueblood... i need to calculate friction factor in spreadsheet so cant use charts... I still cant find a reference for that equation (using massey mechanics of fluids)!

katmar... sure i figured it would be kind of approximate.

I only need to estimate whether rough because apparently:
"At high Reynolds numbers, the sub layer thickness becomes very small and the friction factor f
becomes independent of Re and depends only on the relative roughness height. In this case the pipe is
a hydraulically rough pipe, and Von Karman found that the friction factor f:"
(colebrook-white formula without Re/f term)

I just wanted to do a check in order to use the appropriate equation when calculating f, though maybe it is unnecessary and I can just use C-W for all turbulent cases?

Regards
Chris