Page 285 - HVAC Pump Handbook

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Basics of Pump Application for HVAC Systems

282 The HVAC World

10.4 Proper Use of Affinity Laws

It must be emphasized that the affinity laws apply to pump perfor-
mance alone. They cannot be used directly for calculating pump per-
formance with an actual water system. The reason for this is the fact
that a pump changes its point of operation on its head-flow curve as
the system flow and head change. This point of operation on the pump
head-flow curve can be developed through the use of the affinity laws
as follows:
Referring to the affinity laws (Eqs. 6.1 and 6.2),

Q D h 1 D 2
1
1
1
and
Q D h 2 D 2
2 2 2
and substituting Eq. 6.1 in Eq. 6.2 and transposing, we get

Q 2 h 1
1
2
or Q Q /h h (10.1)
Q 2 h 2 1 2 2 1
2
If Q and h are the desired flow and head, the point of operation on
2 2
the pump head-flow curve, Q and h , can be computed by Eq. 10.1.
1 1
This is accomplished by trial and error, solving for Q by inserting
1
various heads h until the resulting values for Q and h land on the
1 1 1
pump curve.
Referring to Fig. 10.7a, which includes the system head curve of
Fig. 9.1b for the model building of Chap. 9, assume that it is desired
to determine the speed and efficiency of the pump when operating at
500 gal/min and 50 ft of head, point 2, or Q and h . Inserting these
2 2
values in Eq. 10.1, the solution of the equivalent pump flow Q can be
1
achieved by selecting values for h in this equation until Q and h
1 1 1
land on the pump curve. The equivalent point in this case is point 1,
or 561 gal/min at 63 ft. The pump speed would be Q Q 1750
1 2
rev/min, or 561 600 1750, which equals 1636 rev/min. The effi-
ciency of a variable-speed pump would be 83 percent when running at
point 2, which is the efficiency of the pump when operating at point 1
on the 1750-rev/min curve.
If this were a constant-speed pump and it was desired to determine
the impeller diameter that would produce 500 gal/min at 50 ft, Eq. 6.1
would apply, and the impeller diameter would be 561 600 10 in, or
9.35 in. The pump efficiency would be 75 percent at this point. Only
by these equations can pump performance or impeller diameter be
determined. If one were to try to determine pump impeller diameter
by just dividing the two flows, 500 and 600 gal/min, an undercut
impeller would result, namely, 500 600 10 8.33 in.

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