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# Weymouth Formula Example

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## Weymouth Formula Example

(OP)

Hi,

Have located a metric version of the Weymouth formula in ASPE Data Book Volume 2 (screenshot attached).

I am a bit confused about the results I am getting however.

If I enter the following data:

D = 98.34mm
L = 300m
P1 = 70kPa
P2 = 50kPa
S = 0.6

I get 12067601.01 which the formula notes as being L^3/s.

Could it be right that I then need to apply 1/3 as power to get plain l/sec i.e. 12067601.01^(1/3)

If I do I get 229.37 which is 825m3/hr which in turn is 31956 MJ/Hr which sounds about right but don't have anything to check against.

Urgently need a metric Waymouth example with results to check against.

K

### RE: Weymouth Formula Example

This is Weymouth's formula in metric/SI units (source: GPSA, 13th edition):

Q = flow rate of gas, m3/day at base conditions
Ts = base absolute temperature, K
Ps = base absolute pressure, kPa (abs)
E = pipeline efficiency factor (fraction)
P1 = inlet pressure, kPa (abs)
P2 = outlet pressure, kPa (abs)
Lm = length of line, kilometers (km)
γ = relative density of flowing gas (air = 1.0)
T = absolute temperature of flowing gas, K
Zavg = average compressibility factor
d = internal diameter of pipe, mm

You also need to verify if the actual flow conditions fall within range of applicability of Weymouth formula.

Dejan IVANOVIC
Process Engineer, MSChE

### RE: Weymouth Formula Example

I would recommend getting Crane TP 410.

To me, it has been an invaluable resource for understanding and solving compressible fluid issues. It even has an example of using Weymouth and other natural gas equations and compares their results.

### RE: Weymouth Formula Example

Weymouth should not usually be used at pressures or pipe diameters normally found in gas distribution systems. It is more specifically for high pressure, large diameter pipelines.

### RE: Weymouth Formula Example

The original publication said it was valid up to 130 psig (around 10 bara, they didn't specify a minimum pressure), and could not tolerate any CO2 or H2S. I've found that each line segment introduces an additional cumulative error. I don't use it for anything at all.

With today's computers I don't know why anyone would not use the Isothermal Gas Flow Equation and get friction factors from itteratively solving Colebrook. It is a pretty simple solve block and program in MathCad. Even doable in Excel if you hate yourself.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Weymouth Formula Example

I hate myself, apparently; although I now use Goudar-Sonnad for computing Friction Factor to avoid the iteration.

### RE: Weymouth Formula Example

When I use Excel for moderately complex calculations I spend so much time counting parentheses that I just want to cry.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

### RE: Weymouth Formula Example

Avoid the Excel ([]) syndrome by evaluating various terms within separate cells then adding all the formula's terms together in one last cell. You can later and easily copy each cells' contents and replace them into the appropriate term's string in the last cell, if you do only want to have a one-cell formula in the final version.

### RE: Weymouth Formula Example

zdas04 (David)…

I agree with you about using the isothermal gas flow equation. I don't have a warm fuzzy for the empirical gas equations like I do for Hazen-Williams and Mannings for water. It's probably because I do so much more work with water distribution systems and sewer and storm drainage collection systems than I do with natural gas.

You and the others here may interested in some Mathcad worksheets I posted on the PTC Mathcad forums last year on this topic: https://www.ptcusercommunity.com/docs/DOC-5465 (an appraisal of more than two dozen approximations to Colebrook-White) and https://www.ptcusercommunity.com/docs/DOC-6371 (for small natural gas distribution systems). The Mathcad worksheets are Prime 3.0, but for users of other versions of Mathcad and for people who don't use Mathcad, there are also .pdf files for each worksheet. I have also posted Mathcad worksheets on other topics, which you can peruse at your leisure.

Comments and critiques are welcome (especially from experts…i.e., people who used to be perts), either here or on the PTC Mathcad forums.

Fred

==========
"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill

### RE: Weymouth Formula Example

I typically use a spreadsheet that calculates pressure drops using several, sometimes even 8-10 different correlations for the same input data, then I pick the one that gives me the warmest fuzzy in light of the application at hand. That way, if an "expert" comes in and challenges me on whatever correlation I have used, then chances are I've already got the answer using the one the "expert" prefers, too. It is a good way to see where the areas at agreement and the areas of disagreement are between the correlations. It also is a good way to check /verify results.

### RE: Weymouth Formula Example

SNORGY,
Even though I am often the prissy, picky "expert", I used to do much the same thing. Now, when I have to face some jerk as pedantic as I am I show them the results from the Isothermal equation and a list of the things about my problem that make each of the various equations invalid. That happened often enough that I developed this graph for AGA and Panhandle A (I have other graphs for other correlations, this one is kind of the Moody diagram, but I hate Moody's logarithmic y-axis)

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

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