Friction Factor-Simple Pipe Network 1

Friction factor, once turbulent flow has been reached, can vary quite a lot without having all that much direct effect on pressure loss itself. This is especially true when you limit your velocities in your pipe system to those that give reasonable economy of pipe diameters vs pressure drop, when combined with enough velocity to keep the pipes clean, but not too high to erode the pipe walls or to cause high transient pressures when changing flowrates. If your velocities are all over the place, notice I said velocities, not flowrates, then you might want to consider calculating specific friction factors. Take a look at the Moody diagram, once you get out of laminar flow and turn the bend, the curves get relatively flat.

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Thank you, could you just clarify what you mean by ' If your velocities are all over the place' ?

What you're essentially saying is that, we can assume friction factor during turbulent flow i.e Re>4000 because it does not have a great effect on Darcy's equation?

And going back to the last question, how could we amend Hardy Cross, so it is not dependent on friction factor from the start?

Funny that the first line in the Wikipedia article about Hardy Cross is that it is obsolete. That is because it is a tedious, cumbersome, inaccurate method that gave "good enough" answers when there was nothing any better.

As to the Moody diagram, there are no modern pipes that consistently put you to the right of the fully-turbulent line so with modern pipes the stuff that assumes constant friction factors is never really satisfied.

David Simpson, PE
MuleShoe Engineering

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The headloss equations used for modeling piping systems -- whether Darcy, Hazen-Williams, Mannings, whatever -- include a friction factor or roughness coefficient (FF/RC), so you can't ignore it. Period. Deleting the FF/RC requires setting it to zero and this is equivalent to assuming frictionless pipe, which doesn't exist. (Even though the FF/RC is used as a multiplier in Darcy and Hazen-Williams and a divisor in Mannings, setting it to 1 would be mathematically incorrect for frictionless pipe.) If the FF/RC equals zero, there is no valid mathematical solution, so what would be the point of modeling the network anyway?.

However, you can simplify the process by selecting a single representative value for the FF/RC for the entire network. This is commonly done with the Hazen-Williams and Mannings equations when the pipes are all the same material. At worst, you might have several different values in your model based on pipe types. It's really not that big a deal with these two equations.

Darcy presents a more difficult situation because finding the mathematically correct friction factor (as opposed to physically correct) for each pipe involves an iteration (Colebrook-White) inside another iteration (Hardy Cross in your case). That's why selecting a single representative value (or a handful of representative values) is sometimes done when dealing with Darcy and networks. It's also easy to do. You should already know the range of flows, pipe sizes, materials, etc to at least a reasonable level, so pick a few reasonable flow rates, a few pipe sizes, etc and determine a few friction factors. This should provide enough information that you can confidently choose one or a couple friction factors for your pipes.

Personally, I rarely use Darcy and never for modeling water systems. Based on how the equations behave and some literature I have seen that showed how the equations compare to the Moody Diagram, I use Hazen-Williams for municipal distribution (typically <= 24-inch) and Mannings for things like large diameter concrete pipe networks (e.g. irrigation backbones). I usually reserve Darcy for things like pumping station manifold piping and non-water flows.

One other thing, there are better and more robust solution methods than Hardy Cross. If you like free software, I suggest you take a look at EPANET: I have used about a dozen different programs to model water systems, including two Hardy Cross programs I wrote for the HP-41CX calculator (one was a substantial rewrite of the program in HP's HP-41 Hydraulics Solutions book and the other was written specifically for a particular system that I had to analyze for specific regulatory conditions). EPANET doesn't have all the bells and whistles that some programs have but it also doesn't cost hundreds or thousands of dollars.

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"Is it the only lesson of history that mankind is unteachable?"
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I would recommend that you write up a small subroute to evaluate the friction factor e.g. using the formula by Churchill (see here last section).

It dosnt take long to implement, is very roboust and does not require a lot of computational power.

Best regards

Morten

and/or see my spreadsheet for the Colebrook-White friction factor here,


"People will work for you with blood and sweat and tears if they work for what they believe in......" - Simon Sinek

One thing you should consider is the tolerance of wall thickness for seamless and thermoplastic pipes. Wall thisckness tolerance is 12.5% and 11% respectively. The change in diameter due to tolerances has far more impact than changes in fristion factor.

PE manuafacturers with sophisticated instrumentation can produce pipe near to minimum wall thickness without too much trouble. After all PE pipe is just a polymer with energy squeezed into it. Reduce the amount of polymer and the energy to melt same equals greater profit.

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