Tools › Fluids and Heat Transfer › Pumps and Fans › Pump and Fan Performance › Example
Textbook-style centrifugal pump against a 40 ft static head: curve fit, operating point, specific speed, NPSH and the 1,450 rpm affinity scaling
| Tool | Pump and Fan Performance |
| Source | Hydraulic Institute (2019). Rotodynamic Pumps for Nomenclature and Definitions. ANSI/HI 14.1-14.2-2019, Parsippany, NJ (§14.1.4.1 specific speed and type number, §14.2.5.5 NPSHA, §14.2.6.4 power); U.S. Department of Agriculture, Soil Conservation Service (1959). Irrigation Pumping Plants. National Engineering Handbook, Section 15, Chapter 8 (p. 8-4 affinity laws, p. 8-7 example); Rogers, D. H., and Black, R. D. (1993). Reading Pump and Engine Performance Curves. Kansas State University L-886 (affinity example). |
| Level | Undergraduate |
Problem
A centrifugal pump tested at 1,750 rpm with a 13 in impeller gives 150.0 / 148.3 / 143.3 / 135.0 / 123.3 / 108.3 / 90.0 ft of head at 0 / 250 / 500 / 750 / 1,000 / 1,250 / 1,500 gpm with efficiencies 0 / 35 / 60 / 75 / 80 / 75 / 60 %. It pumps 60 °F water (62.4 lb/ft³, vapor pressure 0.26 psi) into a system with 40 ft of static head that needs 100 ft at 1,000 gpm, drawing from an open tank 5 ft below the impeller through a suction line losing 3 ft; the pump needs 12 ft NPSH. Fit the curve, find the operating point, efficiency and shaft power, the best-efficiency point and specific speed, the NPSH available, and the new operating point and the speed that meets the design point if the pump is slowed to 1,450 rpm.
Inputs to Enter
- Curve (gpm, ft, %): 0 150.0 0 / 250 148.3 35 / 500 143.3 60 / 750 135.0 75 / 1000 123.3 80 / 1250 108.3 75 / 1500 90.0 60; reference 1,750 rpm, 13 in; quadratic fit
- Liquid 62.4 lb/ft³, vapor pressure 0.26 psi; system static head 40 ft, design point 1,000 gpm at 100 ft
- Suction: 14.696 psi on the surface, surface 5 ft below the impeller (z_s = −5 ft), suction losses 3 ft, NPSH required 12 ft; new speed 1,450 rpm, same impeller
Answers
- Fit: H(Q) = 150.0 − 5.714 × 10⁻⁵ Q − 2.663 × 10⁻⁵ Q² (ft, gpm), R² = 0.9999995, rms residual 0.014 ft; η(Q) = 0.16 Q − 8 × 10⁻⁵ Q² percent; system K = (100 − 40)/1,000² = 6 × 10⁻⁵ ft/gpm²
- Operating point 1,126.5 gpm at 116.1 ft, η = 0.787, fluid power 33.07 hp, shaft power 42.01 hp; BEP 1,000 gpm at 80 % (operating flow 1.126 × BEP), shut-off 150.0 ft
- Specific speed at BEP: N_s = 1,750 √1,000 / 123.3^0.75 = 1,496 (US), n_s = 28.96 (m³/s, m; ratio 51.645 against the standard's 51.6), type number K = 0.5472 (n_s/K = 52.92)
- NPSH available = (14.696 − 0.26) × 144 / 62.4 − 5 − 3 = 25.3 ft against 12 ft required: margin 13.3 ft, ratio 2.11; suction specific speed 9,110
- 1,450 rpm: k_Q 0.8286, k_H 0.6865, k_P 0.5688; homologous point 933.4 gpm / 79.7 ft / 23.9 hp; new operating point 852.3 gpm at 83.6 ft, η 0.799, 22.5 hp (flow × 0.757, power × 0.536, not the affinity factors, because of the static head); speed through the design point 1,608 rpm
- Two in parallel (option): 1,284 gpm at 139.0 ft, 642 gpm each at η 0.698, 64.6 hp total; two in series: 1,515 gpm at 177.6 ft, 115.6 hp
Notes
The tool's default inputs are this case; press Submit. The pump is illustrative (a textbook-style curve, not a manufacturer's), so the acceptance values are the numpy/scipy solution of the same fit and crossings (References/Pumps-Fans/checks/pumpfan_check.py), the published affinity-law examples (SCS NEH 15-8 Fig. 8-2, KSU L-886: 400 gpm, 50 ft, 6.2 bhp at 1,770 rpm → 332 gpm, 34.5 ft at 1,470 rpm) and the Hydraulic Institute specific-speed factors; test_pump_fan_performance.php, 175 checks. The SCS example of 480 gpm at 180 ft and 73 % → 30 hp is reproduced (29.9 hp).