Mannings Pipe Friction Losses 1

[RjMelbourne]

My Fellow Forum members

I am trying to find the formula for calculating pipe friction losses using mannings. I can find all my uni notes on the Darcy-Weisbach / Colebrook White equations, but nothing on mannings

I have had a project come back from a local authority who has asked for all friction losses to be recalculated using mannings.

From memory the equation is as below. How ever I am not confident that I am correct, and no body where I work can remember the equation either. Unfortunatly as good engieers as my peers are they are all now computer program relient, or have not crunch these sort of numbers in 20 years.

Fiction Loss = Hf
Hf = (19.6 x n^2 x L / R) x (v^2/2g)
Where:-
n = Mannings value
L = Pipe length
R = Hyd Radius
v = Mean pipe vel
g = Gravity

Any help you could offer would be appreciated.

Cheers

Rob

 

[BarryEng]

From Douglas - Fluids, in metric units, Manning: -
v = (R^^0.67 s^^0.5)/n
Where n = 0.009 for glass & 0.022 for dirty cast iron.

I think that in imperial units (if my memory is correct),
v = (R^^0.67 s^^0.5)x(1.486/n)

v = velocity (m/s)
R = hydraulic mean radius (m)
S = slope (m/m)
n = friction value dimensionless

 

[TerryScan]

From a state DOT road design manual:

"Head loss in pipes due to friction can be calculated using Mannings formula, by solving for Sf.

Sf=(Qn/(1.486AR^2/3))^2

where Q = Discharge (cfs;
n = roughness coefficient;
A = cross sectional area (sq.ft.); and
R = hydraulic radisu (D/4 for circular pipes)(ft.).

The head loss is calculated from the formula:
Hf = Sf x L

where L = length of pipe (ft.)"

 

[bimr]

Here is a link to a good demo of mannings:

http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Manning_s_Equation.htm

 

[BarryEng]

If you go back to Chezy (1775), v = C sqrt(R S)
Rewrite as: -
Chezy v = C R^^0.5 S^^0.5
Manning v = C R^^0.67 S^^0.5
Hazen Williams v = C R^^0.67 S^^0.54
etc
etc

These formulae have been derived from model tests.

Only when Colebrook/White came along, were flow formulae based on academic principles rather than based on the results of tests. It is interesting that Hazen Williams was based on tests of (as I remember) 100 mm dia to 300 mm diameter pipes. But I have seen flows from very large pipes, calculated using this formula.

It always worries me when we use values from extrapolation, rather than interpolation, of test data.

 

[cvg]

I have a copy of Hazen Williams book of hydraulic tables. It was originally published in 1905, however it was updated with new data numerous times through 1933. I have the third edition, eleventh printing and according to that, test data from pipe sizes ranging from .5" galvanized pipe all the way to 103" riveted steel pipe was used. In fact, a circular brick tunnel 144" in diameter was also observed, 10 test measurements were made and data was reported. A range of HW "C" values was reported for the tests ranging from a low of 3 to a high of 153. Types of pipe included new, cleaned and tuburculated cast iron pipe; riveted pipe; wooden stave pipe; rectangular unplaned wooden pipes; cement pipe; brick tunnels; wrought iron pipe; galvanized wrought iron pipe; brass, lead, glass pipe; and fire hose. So, in general - the data presented in the book is not extrapolated, but entirely based on hydraulic measurements.

 

[BarryEng]

cvg
That must be an interesting book. I have two (modern) books on fluids that both mention the Hazen Williams original data was derived from 100 to 300 dia. Obviously they were not aware of the book that you have.

By the way - what is the title?

On the subject of testing, we tried testing (for a HW coefficient) a DN1500 pipe (many years ago) & it was very difficult, even over long distances. We had a trunk main with no offtakes, a meter that was a dall-orifice that had a + or - error of 2% (reasonable for an inferential meter), mirror backed gauges with + or - 1/4% error, & accurately levelled meter sites, & even with these small errors, there was quite a large range of results.

 

[cvg]

see the attached file for the book title page

 

[RWF7437]

Isn't the Colebrook White equation also empirical ? What's wrong with using empirical equations anyway ? This is engineering, not science.

 

[BarryEng]

cvg
Very interesting. Thank you for the details. I will try to find a copy. I like historical info to guide me (as does 'slideruleera' in his website), to appreciate the long path (usually) to the 'modern' formulae.

RWF7437
I agree - that there is nothing wrong with empirical equations. It was just that all of the 'old' flow formulae were based on tests & fitting a formula to the data. Colebrook White at least brought some rationalisation into the derivation of the values rather than 'curve fit' of the data.

Having said that, a great many flow formula that are based on rational (or dimensional) analysis, still have a "C" or a "K" in front to take care of "other" parameters that were (probably) unknown at the time of derivation. The C or K (empirical values or 'fudge' values) are still needed to produce correct results that reflect the real world.

The reason that I mentioned above, about the testing that was done to find a HW coefficient for a large pipe, & the accuracy that we used, resulted in values that were not really remote from the formula attributed to Chezy in 1775. For most flow calculations in relatively short pipes, Chezy is probably as good as anything else.

 

[RWF7437]

Thanks BarryEng,

My own preferences are the Manning Equation or the Darcy Weisbach Eq. using either the published values for "n" and "f" friction factors, or the Moody Diagram. This avoids the iterative solution required by the Colebrook White equation. For most conduits, pipes and incompressible fluids these will usually get one "close enough". Any of these are "rational" enough for most things.

The H-W method is only accurate (+/- 15%) for water at normal temperatures and for the range of flows and conduit shapes tested originally, as far as I know. Still, some reviewing agencies know nothing else.

I wonder if RJMelbourne still cares about any of this fascinating discussion ?

 

[BarryEng]

RWF7437
Probably not.

Another thing about HW coefficients, in the original derivation, the condition of the pipe is the only parameter for its selection. In actual fact, the HW coeffic varies with Reynolds number, but as I said above, this small error would have been masked by variations in the test results. Hence there should have been a "Moody" type diagram for HW if it had been based on a rationalisatation type of formula instead of a best fit of test data.

It comes back to the fact that very few people actually check (or know), to see if their calcs are correct or whether variations in flow (in the real world) mask the accurate values.

I suppose that the modern use of mag flow meters (with better accuracies) rather than inferential type meters, might increase awareness in actual results, especially in long pipelines.

 

[jartgo]

Recall from early hydraulics classes that the S term in Manning's is the slope of the hydraulic grade line, not the slope of the pipe. In open channel hydraulics the two are usually the same, so that in most uses of Manning's (gravity flow situations) we assume that S is equal to the slope of the pipe.

So, using manning's, the friction loss can be computed from the S (slope) required to move the flow through the system. That is, you know what Q is, you presumably know what the other parameters are, then solve for S. I haven't checked it, but it appears Terryscan has already rearranged the equation for you in terms of S. This will give you the slope of the hydraulic grade line and from that and the length of pipe, you can calculate what the friction loss would be in terms of feet or meters.