อัปเดต 2026-09-07

Pump Sizing

NPSHa (Crane TP-410) + operating point

Sizes a centrifugal pump against a system curve: computes NPSHa at the suction, fits a parabolic vendor pump curve, finds the operating point where pump and system curves intersect, and derives shaft power via a Karassik efficiency approximation.

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Closed-form algebra throughout — no iteration. NPSHa is a 4-term head balance (atmospheric + source gauge − vapor ± static − friction). The pump curve is exact-fit at shutoff (Q=0) and BEP; the system curve is static head + k·Q². Their intersection is solved analytically for Q², then substituted back for H.

สมการ

NPSHa head balance (Crane TP-410)

N P S H a = \frac{P _{a t m} + P _{g, sr c} - P _{v a p or}}{ρ g} \pm h_{s t a t i c} - h_{f, s u c t i o n}

+ for flooded suction (liquid above pump CL), − for suction lift. Friction always subtracts. Matches the backend pump_advanced.py cavitation check.

Pump curve — 2-point parabolic fit

H (Q) = H_{0} - (H_{0} - H_{b e p}) (\frac{Q}{Q _{b e p}})^{2}

Exact at shutoff (Q=0 → H=H_0) and at BEP (Q=Q_bep → H=H_bep); monotone-decreasing beyond BEP.

Operating point (pump ∩ system curve)

Q_{o p}^{2} = \frac{H _{0} - H _{s t a t i c}}{\frac{H _{0} - H _{b e p}}{Q _{b e p}^{2}} + k}, H_{sy s} (Q) = H_{s t a t i c} + k Q^{2}

Closed-form intersection of the parabolic pump curve and the quadratic system curve; k aggregates Darcy-Weisbach (Swamee-Jain) + ΣK minor losses. Returns no-flow when H_static ≥ H_0.

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