Back calculating surface roughness 1

[kapo84]

thread378-220785

I have read a number of posts on this site which mention "back calculating" to find the roughness of a pipe/hose (see link). I have a fabric duct used for HVAC which was sent to us for R&D purposes from the manufacturer. I am having trouble back calculating my test results to find the duct roughness. It's a simple fix surely -- can someone outline in detail their process for calculating epsilon?

Thanks in advance

 

[BigInch]

Probably easier to assume an initial value for [ε] and iterate with it until you get the observed pressure drop.

Solving a Colebrook or similar fluid head loss equation for [ε] isn't on my priority list.

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[kapo84]

I will try iterating ... I solved the Haaland equation for ? and, as I mentioned earlier, saw results which were not realistic.

 

[vzeos]

kapo84,

For flow in a duct the flow is probably fully turbulent and you can use the rough pipe law:

1/[√]f = 2Log (3.7D/k_e) or
(1/2)1/[√]f = Log (3.7D/k_e)

Take the anti log of both sides and get:

10^{(1/2)1/[√]f}=(3.7D/k_e)

Solve for k_e:

k_e=(3.7D/10^{(1/2)1/[√]f})

f is the Darcy friction factor
D is the pipe diameter
k_e is the effective roughness

You can do the same for the Colebrook equation.

 

[kapo84]

vzeos:

Thanks for the help! I iterated per the instructions of BigInch and received the results I needed.

The equation you provided gave me near exact results to those which I iterated. However, it is handy to have an equation which Excel can equate for large amounts of data.

In hind sight I should have tried to solve for the Colebrook equation rather than the Haaland equation since the Haaland equation is derived from the Colebrook equation.

Thanks again BigInch and vzeos.