Isn't that what the iterations in the calculator are for? I don't know how it's written (code), but if it's doing iterations it would seem like it is assuming a flow, calculating the head loss, using the new reduced flow, recalculating the losses, etc.
Before the advent of the personal computer, the Hazen-Williams formula was the most used with piping engineers. They like it due to the relative simplicity of the calculations. However, it was inherently inaccurate, due to the reliance on a friction factor that could vary anywhere from 80 - 130, depending on the pipe material, pipe size, and fluid velocity.
Another formula for calculating head loss, is the Darcy-Weisbach fromula. It is more difficult to work with, however, with computers, it is now the standard with hydraulic engineers. It still lacks a provision for accurate determination of the friction factor, though.
The friction factor can be determined with accuracy using a Moody Chart, which is based on the Cole-White equation for calculating the friction loss for turbulent flow in a pipe. Due to the structure of the equation it requires an iterative solution. The result is plugged into the Darcy-Weisbach formula. You come up with a fairly accurate result.
Since the calculator is using an iterative process, I would think it is plugging the result from the Cole-white equation into a Darcy-Weisbach equation, or a derivative of them. But I could be way wrong. Still, my question would be: But where is it getting the velocity (flow rate) from?
The thing is, engineers don't grab a pump and say "what will this pump do in this piping system?" You don't need math (well complex math anyway) because the answer can be directly measured. Apply it to the pump curve--Idealized as the pump curve may be--and it gives you the total head loss of the system--subtract the vertical lift, and you have the friction loss (in vertical feet)
At the same time, a hobbyist asking what will this pump do in this system, is an unanswerable question. It can be directly measured, by testing, certainly. But in the theoretical realm, it is unknown. Why? Because you don't have flow rate. The only thing that is constant at any point in a piping system is the flow rate, everything else varies with the flow rate.
A pump curve cannot be used. The pump curve starts at 0' TOTAL head loss, and pump output decreases as TOTAL head loss increases, but there is no friction factor involved e.g. no pipe. As soon as you add a 1" piece of pipe, the pump still flows on the flow curve, however friction loss has been introduced, and head height has increased, so the total head loss will be greater than 1". (With some pumps, even the wrong pipe size will complicate the problem.) Therefore, you don't know the velocity (flow rate) so the total head loss cannot be calculated, because it is based on the velocity. It can only be guessed at. You have introduced error to the equation, it can be insignificant, (the 1" piece of pipe) or it can cost you 5 or 600 gph, or more, depending. My classic real world example being the 1500gph pump @ 14' vertical lift, by the flow curve, operating at shut off head height of ~42'--with only a 14' vertical lift. (A basement sump, over under around and through piping system)
In actual practice, these things are applied with a specific flow rate in mind, and a specific plumbing system at least designed, and the engineer can tell you "You need to use pump B, because pump A won't do it." The system can then be redesigned so pump A, will get the job done: increase the pipe size, reroute it, less fittings, what have you. Even then pump A may not do it. So pump B it is. They are asking what do I need to get the water to go this fast, in this piping system.
It is not all that complicated really, as the Darcy-Weisbach and Cole-White formula results can be found in "friction loss charts," reducing the mathematics to simple addition, subtraction, multiplication, and division. The only problem with that, is the charts are generally separated by 5 gph calculation points. i.e. 5, 10, 15, 20 gpm etc. (gallons per minute) so falling in between gives an error factor. The result you are looking for, is I need a pump that will push X gallons per minute @ Y' total head (vertical lift + friction loss converted to vertical lift.)
IMO, this is a better way to approach the problem, and it will give better final results, and then get opinions on the quality of a selection of pumps that you already know will do what you want them to do. Adding branches complicates things a bit, but still--logically-- working through the simple math will give you the result you need. Then when someone suggests you use a pump that you know does not have enough umph, it makes the selection process less of a chore. Eheim may be a good pump, but it may not do what YOU need it to do, Mag pumps might be good pumps, but unless you use 1.5" pipe, it won't do what you want it to do--and even then it still might not.
