Oldhydroman, that is a good pdf file but it doesn't have anything on hoses. There is an equation called poiseuille's law for laminar flow in pipes and hose. The problem is that the manufacturers don't supply the pressure drop per length per flow. One must find this out empirically. Another hose manufacturer deficiency is they don't provide the capacitance of their hose. Again, one must find this out empirically.
The "scholarly" article I previously attached derives from first principles the pressure drop caused by flow through a "line". I suppose it doesn't help that the author then starts writing about a "pipe" but the physics is the same regardless of the materials of construction, i.e., the uniform circular cross section "line" could be made of metal, concrete, wood or ... rubber. But you're both right, the article didn't actually contain the word "hose".
For any fluid carrying "conduit" [I'm trying to choose a generic term here rather than referring to something electricians run cables in], the extra pressure drop by virtue of the roughness of the inside surface is accounted for in the friction factor (for turbulent flow). We would normally expect the inside surface finish of a [serviceable] hose to be as smooth as that of a rigid steel pipe or tube so that means it makes no difference to the calculations of pressure drop in a "hose" or a "pipe".
Flexible hoses do differ from rigid pipes in the extent to which they change volume under pressure but the dilation or capacitance of the hose [usually ignored for the purposes of pressure drop calculations] is taken into account in equation 3.5 ("the flow consumed by the expansion of the control volume"). In practice, once you've pressurized the hose, its diameter will have set itself to a relatively constant value along its length (if the end-to-end pressure drop is small in comparison to the inside-to-outside differential pressure). This new diameter can be used in the pressure drop calculations if you like, but it's still the same equations for pipes and hoses. So for steady state conditions the differing capacitance values of pipes and hoses is of no consequence.
If you take the friction factor as 64/Re (for laminar flow) and put this into equation 3.10 you will actually get a version of Poiseuille's formula.
If you want to determine the pressure drop for turbulent flow you need to look up the friction factor on a Moody diagram. When you use this sort of friction factor in equation 3.10 you get a rearranged version of the Darcy-Weisbach formula.
For the sort of "conduits" used in fluid power systems and the typical Reynold's numbers in those systems it is quite adequate to use the Blasius formula to give you a suitable friction factor (the second part of equation 3.11). This avoids going cross-eyed trying to read a Moody diagram.
Note that equation 3.10 could be thought of as "pressure drop per unit length", unless the original author wrote "l/d" when they meant "L/d" and this got accidentally printed as "1/d".
Sarakhan, now I've seen the links you're looking at I think I may have something more along the lines of your search - but it'll be a few more hours before I can post it. In answer to your specific question: all of these equations are applicable to hoses.
You can take bends and fittings into account [approximately] by adding an equivalent length to your "conduit". So we might say, for example, that the pressure drop caused by having a compact 90 degree elbow on the end of a hose is equivalent to an extra 70 diameters added to the length of the hose (offhand I think it's 70 but please don't hold me to account on that number). So if your 1" hose were 100" long in total but you had one of these elbows on one end then you would calculate the pressure drop assuming that the equivalent length of the hose was 170".
There is a method of taking into account the fact that the hose itself is probably following a curved route - and the tighter the curve the more pressure drop you will get. Not many people bother with that level of sophistication because the other parts of the calculation aren't accurate enough to warrant such attention to detail. Specifically; in the world of hydraulic oil, working temperature (hence fluid viscosity) is usually a bit of a guess, and the viscosity of the brand new fluid the blender pours into the barrel is itself subject to a +/- 10% tolerance even before your client has changed the viscosity slightly as a result of shear-thinning/aging/heat damage and contamination. The calculations used to translate any particular temperature to a new viscosity are a bit empirical and rely on the viscosity index being known accurately (I don't suppose it is). Then you need to modify the viscosity and density figures based on actual pressure. And if we want to be particularly pedantic, the temperature of the fluid (hence viscosity, volume and density) changes along the length of the "conduit" because of the pressure loss being exhibited as a heating of the fluid. I'm sure there's some software out there that will do a brilliant job of working it all out to twenty decimal places but I find myself asking how accurate the answer really has to be.
I've never found hose manufacturer's pressure drop charts very trustworthy. If they were to give a chart of pressure drop per length per unit flow (some do) then you would still have to modify it for changes in viscosity (and density) and you would be unsure exactly where the increasing flow rate caused the flow to go turbulent - and this would change all the numbers on the chart anyway. Putting the numbers in your own calculation gives you a better feel for what is happening.
I do agree, however, that it would sometimes be helpful to be told the capacitance of the hose - particularly for stability/stiffness calculations. But then I ask myself if the hose manufacturers really know themselves and if any "capacitance" value they could give would itself be a function of batch number, pressure, temperature, bend radius and service life.
Let me know if you want the artisans version of the pressure drop calculations rather than the physicists. My version is geared towards fluid power circuits running on mineral oil - is that what you're looking for?
