when to use C or reynolds number when calculating head loss

[ketanco]

in question 17-2 of practice problems for the civil engineering pe exam by michael lindendburg, 13th edition, there is a pipe that connects points A and B. it gives pipe length, diameter, pipe material, temperature of water and the flow rate Q. B is 60 feet above Point A. it asks the pressure at point A if the pressure B is 50..

when i did this, i used C from the tables, coefficient of friction for the steel pipe in order to calculate the head loss. i didnt use the temperature at all. but they used the temperature information and did it by calculating reynolds number. how do we know when we use C or reynolds number when calculating the head loss hf? why didnt they use the formula with the L, C, V, D to calculate the head loss? I used that one and still was able to calculate something. although it was wrong. they used the Reynolds number. I didnt understand why

 

[BigInch]

What temperature is the water?

Independent events are seldomly independent.

 

[ketanco]

they give the temperature as 60F

 

[Ron]

It has been a long time since I've dealt with this but if the pipe is a large diameter and not flowing full, that is likely why the Reynolds number was used. For smaller diameter pipes or pipes flowing full, C is used. Rusty memory, so don't bank on it!

 

[beej67]

"C" as in Chezy C?

Disclaimer - this is all from memory, I'm away from my texts this morning. If I recall correctly, the formulations of both the Chezy equation and Manning's equation are based on the Darcy-Weisbach equation, which relates friction loss to Reynolds number, but Chezy and Mannings both make assumptions to get you away from the Moody Diagram. Using D-W, you'd pull your Darcy friction factor from the Moody diagram after determining Reynolds number, which can be a real pain in the ass because you don't know the velocity until you determine the friction, so you have to guess at the Reynolds number and check, iterating a few times with the Moody Diagram. Using Chezy or Mannings you get to skip that step because the formulations have built in approximates for your friction factor based on an assumption. (I think they're based on the Colebrook equations? Again, this is from memory) That makes the math a hell of a lot easier and less iterative, but it also means it's only valid for certain ranges of Reynolds number. If I recall, both Chezy and Mannings are for fully rough turbulent flow, although there may be an alternate derivation of Chezy for smooth flow. I'm sure about Mannings, but I'm a little foggier on Chezy, and haven't had my coffee yet.

So short answer is this - don't use Chezy or Mannings unless you check your Re and confirm that the equations are valid for your case. For the PE exam, I would always use D-W if they give you all the info you need to use it, because chances are they're only going to give you all that info if you need it.

Of interest to practicing engineers - when sizing pipes, folks in practice very rarely check their Reynolds numbers to see whether Manning's Equation is valid. At least in Civil anyway. And for flatter, smaller, smoother pipes, say 12" PVC at less than 1%, you're pushing the boundary of that assumption and would need to switch over to D-W. There's a lot of pipe in the ground based on the wrong equation.

(moody diagram)

http://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Moody_diagram.jpg/1024px-Moody_diagram.jpg

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[cvg]

there are numerous methods to calculate head loss. it's very possible that C is Hazen-Williams "C" factor, not Chezy "C" factor. Hazen and Williams were attempting to come up with a more reliable method of estimating headloss (than the Chezy method which had considerable variability in the c value and which is also related to the hydraulic radius and the slope) when they started research in 1903.

 

[beej67]

Good call. I'd forgotten about Hazen-Williams.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com