you need to verify minor loss for PVC fittings? It makes little difference what material the fitting is since the distance flow travels is so small in comparison the the loss associated with the fitting, so we usually factor that out of the head loss calculation....Does this answer your question? I am not sure from the way you worded it...
I agree with BobPE - the material will not have a significant effect on the K value. The K value is the number of velocity heads lost and is not influenced by the friction factor.
This is sometimes confusing when using the Crane 410 procedures. The way Crane correlates the K value it does seem to be affected by the friction factor - but this is just a "standard" friction factor that Crane have chosen to use and it has nothing to do with the actual friction factor (or pipe roughness) of the actual material. The Crane manual is a great resource, but this particular aspect has caused a lot of confusion over what really influences the K values.
In addition we could add that, in theory, K is independent of the size of geometrically similar fittings. However, in practice, it has been shown that the larger the size the lower the value of K.
Besides, there are tables that correlate K with Le/D in the Darcy formula for friction drop. The error range in doing so seems to be sometimes +/- 30%.
I've found an article in the Chemical Engineering issue of July 1999 titled Correlate Pressure Drops through Fittings by Ron Darby of the TEXAS A&M University, that apparently wraps up the subject under consideration.
The author claims that calculating the "loss coefficient" Kf in the irreversible energy dissipated by friction, ef = [Σ]Kfi Vi2/2, by using three constants based on the type of fitting, its diameter and the Reynolds number, which also depends on flow rates, shows an excellent fit.
He states that other (obsolete) methods for estimating the loss coefficient, such as those based on tabulated single values, or even those given by Crane which are based on the friction factor of fully turbulent flows on Sch 40 clean pipes, and on the (L/D)eq of the fitting, fall short because they use one or two constants to characterize the loss coefficient and do not reflect the full influence of the Reynolds number.
The author submits a comparison on the flow rates for water -estimated on a particular example for Reynolds number ranging from 393 to 13,100 and pipe sizes from 1-in. to 12-in.- showing under- and over-predictions resulting from using other procedures vs his proposal.
His 3-K equation appears to have a very good statistical accuracy of the fit as measured by r2.
The value of the dimensionless loss coefficient is obtained from a formula such as:
Kf = Km/NRe + Ki(1 + Kd/D0.3)
The author provides formulas, tables and graphs for the constants in this formula.
Q = flowrate, CFS
[Δ]Z = change in elevation, ft
D = diameter of pipe, ft
g = gravitational acceleration 32.2 f/s2
Kfi=loss coefficient for each of the pipe system elements, dimensionless.
A thing to bear in mind in injection moulded uPVC fittings the losses in elbows is higher than for a steel fitting. The radious is reduced and where the pipe is solvent cemented in there is a gap and then a sharp edge. The losses can be significantly higher. I use 40f for such fittings. Tees are not as bad but I would use 30f and 60f for straight thru and branch respectively.
Reducers need to be considered by type. Some fittings are purely a reducing bush with a steep change in cross section. tapered fittings are generally similar to a steel fitting. The Crane 410 procedure can be used to determine the factor x f.
Losses at valves may also be increased because of the change in diameter from the bore of PVC to the body of a valve that may have its design roots in ductile or cast iron pipe. The changes in diameters are sharp edge and do cause turbulence.
The other problems with uPVC pipe is the high tolerances on wall thickness. Some manufacturers will rationalise their sizes. When you specify a class 6 and a class 9 or 12 may be supplied depending upon what is in stock and if the supplier wants the sale. That said, smart manufacturers will always make pipe to "lean" tolerances and give you the minimum but you have to be careful. After all the production costs are for resin and the energy to change from crytals to pipe shape. The higher the mass the higher their costs. Make sure the certificates for the material match your calculations.
