ASHRAE Journal - May 2024 - 38

TECHNICAL FEATURE
FIGURE 5 Pump BHP based on speed.
8
7
6
5
4
3
2
1
200
400
600
0 ft Min Head
Exponent of 3
FIGURE 6 Pump BHP based on flow.
8
7
6
5
4
3
2
1
100
200
0 ft Min Head
Exponent of 3
100
80
60
40
20
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
VFD Speed
Mfr Data-Linear Setting
Mfr Data-Squared Setting
2.2 Speed-to-Power Exponent
2.7 Speed-to-Power Exponent
flow and 3 in. static pressure (747 Pa). The manufacturer
provided BHP and speed data for the points shown in
Figure 1. Three cases were considered: 0 in., 0.75 in. and
1.5 in. minimum duct static pressure (0 Pa, 187 Pa and
374 Pa). The system curves assume the minimum values
at zero flow, 3 in. static pressure (747 Pa) at full flow and
a squared pressure-to-flow relationship in between.
Maxwell3 describesthis method of estimating fan static
pressure with a fixed duct static pressure setpoint.
The manufacturer-provided BHP and speed data at
the points shown in Figure 1 (page 36) are shown in Figure
2. BHP varies as the cube of speed in all three cases; the
minimum static level does not have an impact on the
speed-to-BHP exponent. The speed-to-BHP exponent
of 3 from the manufacturer-provided data is close to
38
ASHRAE JOURNAL ashrae.org MAY 2024
300
Pump Flow, gpm
Exponent of 2
10 ft Min Head
FIGURE 7 VFD power draw varies with V/Hz setting.
30 ft Min Head
400
500
600
800
1,000
Pump Speed, rpm
Exponent of 2
10 ft Min Head
30 ft Min Head
1,200
1,400
1,600 1,800
the speed-to-power exponent of 2.7 found using the
metered data mentioned previously. The BHP exponent
is higher than the power exponent since BHP does not
account for reduced motor, VFD and belt efficiency at
reduced loads.
The manufacturer-provided BHP and airflow data at
the points shown in Figure 1 are shown in Figure 3. The
effective flow-to-power exponent varies depending on
the minimum static pressure setpoint. This agrees with
the monitored data shown earlier-the flow-to-power
exponent is lower than the speed-to-power exponent.
For systems that have a minimum static pressure above
0 in. w.g. (0 Pa), a cubic or near-cubic relationship
between flow and BHP should not be assumed.
Pump
For the pump, a base-mounted end suction centrifugal
pump with an 8.25 in. (210 mm) impeller was selected,
at 500 gpm (1893 L/m) flow and 50 ft head (149 kPa).
The manufacturer provided BHP and speed data for the
points shown in Figure 4. That data is shown in Figure 5
and Figure 6. Similar to the fan:
* Three cases were considered: 0 ft, 10 ft and 30 ft
minimum head (0 kPa, 30 kPa, 90 kPa). The system
curves assume the minimum values at zero flow, 50 ft
head (149 kPa) at full flow and a squared pressure-toflow
relationship in between.
* The minimum head level does not have an impact
on the speed-to-BHP exponent. It's not clear why the
manufacturer's data shows an effective exponent greater
than 3 for the 30 ft (90 kPa) minimum head case.
* The speed-to-BHP exponent of 3 from the
manufacturer-provided data is close to the speed-topower
exponent of 2.7 found using the metered data
mentioned previously.
* The effective flow-to-power exponent varies
depending on the minimum head pressure setpoint.
This agrees with the monitored data discussed earlier-
the flow-to-power exponent is lower than the speed-topower
exponent. For systems that have a minimum head
pressure above 0 ft, a cubic or near-cubic relationship
between flow and BHP should not be assumed.
VFD Torque Settings
VFDs serving variable torque loads such as centrifugal
and axial fans and pumps should have their torque
or V/Hz settings set to " variable " or " squared " for
% of 100% Speed Power
Power, BHP
Power, BHP
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ASHRAE Journal - May 2024

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