The H-Factor

This was written by a coworker – Steve Downing – for a customer who had to have an answer for the AHJ as to why the equivalent lengths for C100 piping are less than those for C140:

'The fitting equivalent length modifiers were intended to keep the friction loss (Pf) thru a given size fitting as a constant for any given flow regardless of what kind of pipe it is attached to or what the C-factor of that pipe is when calculated with the Hazen- Williams formula.  It is done by altering the fitting length based on the internal diameter and C-factor of the pipe it is attached to.  This is because the loss thru a fitting is not dependant on the type of pipe attached to it or that pipes C-factor, but in fact is a constant based on flow and caused because the water is forced to make a turn.

These two modifiers are found detailed in paragraph 22.4.3.1.3.1,  paragraph 22.4.3.2, and paragraph 22.4.3.2.1 of NFPA 13 (2010 Edition) and apply to all fittings except copper and plastic for which different equivalent length tables are provide by the manufactures.

Let's take an example and see how this works.  Let's assume a 1" Tee with 40 gallons running thru it that's attached to a 1" piece of Schedule 40 with an internal diameter of 1.049 and a C-factor of 120.  Based on the equivalent length of 5 feet from table 22.4.3.1.1, the Pf for such a fitting would be 2.3456

Now, let’s make the C-factor be 100 and redo the calculation.  Our 5 foot fitting now becomes 3.568 based on a modifier of .713 from table 22.4.3.2.1.  This results in a Pf of 2.343.  So, the C-factor portion of the modification does in fact hold the Pf's the same for all practical purposes.

Now, let’s return to a C-factor of 120, but make the pipe be Schedule 10, which has an internal diameter of 1.097.  The fitting modifier from paragraph 22.4.3.1.3.1 is 1.243 which makes our 5 foot fitting into a 6.217 foot fitting.  Now plugging that into the 

Hazen-Williams formula results in a Pf of 2.3455.  So again, the Pf remains essentially the same.

Finally, let's use both Schedule 10 and a C-Factor of 100.  The new equivalent length is 4.4329 based on using both modifiers and the Pf is 2.343, which is again essentially the  same.

The very small difference in the second and forth calculation is attributable to the modifier of .713 listed in NFPA 13.  This number should actually be .713698 or .7137 when rounded based on the formula (Cnew / 120)^1.85 power.  If .7137 was used the two resultant Pf's would be 2.3456 and 2.3456 which would bring them in line with the others.

However, even with this discrepancy, the NFPA modifiers do in fact result in essentially the same Pf thru a fitting regardless of what kind of pipe it is attached to or what C-factor it is used with even though the fitting equivalent lengths will appear to vary from that used with Schedule 40 and a C-factor of 120"