Page 116 - Know and Understand Centrifugal Pumps

The System Curve

an approximation, it is most precise with velocities between 3 and 9 feet
per second in pipes with diameters between 8 and 60 inches.

The Darcy/Weisbach Formula
This formula is another variation on the Affinity Laws. Monsieur's
Darcy and Weisbach were hydraulic civil engineers in France in the mid
1850s (some 50 years before Mr. H & W). They based their formulas
on friction losses of water moving in open canals. They applied other
friction coefficients from some private experimentation, and developed
their formulas for friction losses in closed aqueduct tubes. Through the
years, their coefficients have evolved to incorporate the concepts of
laminar and turbulent flow, variations in viscosity, temperature, and
even piping with non uniform (rough) internal surface finishes. With so
many variables and coefficients, the D/W formula only became
practical and popular after the invention of the electronic calculator.
The D/W formula is extensive and complicated, compared to the
empirical estimations of Mr. H & W.

The merits of the Hazen and Williams's formula versus the Darcy/Weisbach formula
are discussed and argued interminably among civil engineers. It is our opinion that if
a student learned one method from his university professor, normally that student
will prefer to continue using that method. The two formulas are variations on the
Affinity Laws, which are probably equally adequate to 'guestimate' the friction losses
in non-uniform piping. Both the H Et W and D/W formulas try to approximate the
friction losses (Hf and Hv) in a piping system that physically does not exist. It doesn't
exist because these calculations occur during the design phase of a new installation.
But in this phase, it is necessary to begin specifying the pumps, although based on
incomplete information. It's somewhat like a blind man throwing an invisible dart at
a moving dartboard.

It really doesn't matter which formula (the H & W or the D/W) one
prefers to use in calculating friction losses (Hf and Hv) in a pipe. Both
formulas have deficiencies. Both formulas assume that all valves in the
system are completely and totally open (and this is almost never the
case). Both formulas assume that all instructions on construction and
assembly (the pipes, supports, connections, valves, elbows, flanges and
accessories) are followed to the letter (practically never). Both formulas
assume that there are no substitutions during construction and
assembly due to back orders and delivery shortages (Yeah, right!).
Neither formula considers that scale forms inside the piping and that
the interior diameters, thus Hf and Hv, will change over time. Neither
formula considers that control valves are constantly manipulated, nor
that filters clog. One formula doesn't consider that viscosity, thus stress