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Affinity laws, pump and fan power and efficiency, NPSH and cavitation, operating point, parallel/series operation, and compressor work.
5 concepts
The affinity laws (flow ∝ N, head ∝ N², power ∝ N³), riding the pump/fan curve, and why a VFD beats a throttling valve on energy.
Fixed impeller, variable speed (rpm). Flow linear, head/pressure square, power cube. Valid at constant efficiency.
Steady-state flow is the intersection of pump/fan curve and system curve. Affinity scaling moves the machine curve; the system curve is unchanged.
Slowing a pump with a VFD
Problem. A circulating pump at delivers at of head and draws . The loop is all friction (no static lift). A VFD slows it to . Find the new flow, head, and brake horsepower.
VFD savings versus an outlet damper
Problem. A supply fan delivers at drawing on a friction-dominated VAV duct system. The load drops and only is needed. Estimate the fan power if flow is cut with (a) a VFD and (b) an outlet damper that throttles to
Impeller trim to hit a duty point
Problem. A pump with a impeller produces at but the friction-only system needs only at that reduced flow. Find the trimmed diameter (assume the duty point stays on the affinity parabola) and the new flow.
Hydraulic vs brake vs input power, the GPM·ft/3960 and CFM·in.wg/6356 work shortcuts, and NPSH available vs required to stop cavitation.
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The system resistance curve H ∝ Q², where it meets the pump/fan curve, throttling vs speed control, and why parallel adds flow while series adds head.
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Centrifugal (FC/BI/airfoil) vs axial fans, reading the fan curve and its stable region, class and arrangement, and fan total vs static efficiency.
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Isentropic vs polytropic compression work, pressure ratio and staging with intercooling, volumetric efficiency and clearance, and reciprocating vs centrifugal/screw machines.
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Fixed speed, trimmed impeller diameter . Same 1-2-3 exponents as speed change.
Head in feet of fluid is density-independent; pressure (psi) and brake horsepower scale linearly with .
= fan total, static, or velocity pressure (in. wg). Fan pressure also scales with air density — important at altitude or elevated temperature.
Fan shaft power scales with speed cubed and linearly with air density. Per NCEES §9.3.8.3 (dry standard air, 14.696 psia, 70°F unless stated).
VFD savings estimate on a friction-dominated system ( through the origin). Overstates savings if static head is present.
Combines the flow and head laws; eliminating shows affinity-scaled points lie on a parabola through the origin.