Controlled operating-point calculation
Documented Pump Hydraulic & Input Power Worksheet
Calculate power transferred to a steady liquid and the corresponding pump input power from one documented operating point. No catalogue efficiency, hidden gravity value or motor-sizing margin is supplied.
Operating-point power record
Steady-liquid energy relation
ηp = Pw / Pp
Pp = Pw / ηp
e = gH and Δpequiv = ρgH
Pw is pump output power transferred to the liquid in watts; Pp is pump input power at the documented complete-pump boundary; ρ is liquid mass density in kg/m³; g is acceleration in m/s²; Q is volume flow in m³/s; H is pump total head in metres; and ηp is a dimensionless pump efficiency entered as percent.
Dimensional check: (kg/m³)(m/s²)(m³/s)(m) = kg·m²/s³ = W. Also, gH has J/kg and ρgH has Pa. The pressure-equivalent output is an energy equivalence, not an assertion that a single gauge pressure equals pump total head; velocity, elevation and reference conditions belong in the total-head determination.
适用性
The calculation is a general reference relation for a steady, effectively incompressible liquid operating point. Q, H, ρ and ηp must be compatible values for the same pump, speed, impeller, liquid state and boundary. Viscosity can change flow, head, efficiency, NPSHR and power. Multiphase, compressible, transient, slurry and non-Newtonian cases require the applicable method and controlled data.
| 数量 | Conversion used | 基础 |
|---|---|---|
| Flow | 1 m³/h = 1/3600 m³/s; 1 L/s = 0.001 m³/s; 1 U.S. gal = 0.003785411784 m³ exactly | SI definitions and exact U.S. liquid gallon |
| Length/head | 1 英尺 = 0.3048 米 | International foot |
| Mass density | 1 lb/ft³ = 0.45359237 / 0.3048³ = 16.01846337396014 kg/m³ | Exact avoirdupois pound and international foot |
| Power display | 1 mechanical hp (550 ft·lbf/s) = 745.6998715822702 W | Exact pound/foot definitions with conventional standard gravity |
| Pressure display | 1 psi = 6894.757293168361 Pa | lbf/in² under conventional standard gravity |
Mechanical horsepower is stated explicitly because “hp” can denote different units. The worksheet retains SI internally and only converts the displayed result.
Official formula references
The Hydraulic Institute’s official Pump System Certification Formula Reference Sheet, Version 1 gives Pw = QHρg/1000 for kW with Q in m³/s, H in m, ρ in kg/m³, and Pp = Pw/η. The U.S. Department of Energy’s published Energy Conservation Program: Test Procedure for Pumps final rule, equation (10), independently states Pu = ρQHg using pump total head.
Definitions and operating-point control
The Hydraulic Institute Data Tool definitions define total head as liquid energy increase per unit weight, pump efficiency as output power divided by input power, pump input power at the complete-pump boundary, and rate of flow at suction conditions. Its pump-curves guidance shows head, efficiency and input power as functions of flow at a specified speed and warns that viscosity affects performance.
ISO boundary
ISO 9906:2012, Edition 2 remains Published and is at close-of-review stage 90.60. It covers hydraulic performance acceptance tests for rotodynamic pumps and defined acceptance grades. This open worksheet does not reproduce its licensed procedure, tolerances, instrumentation requirements or acceptance rules; those details are NEEDS_LICENSED_SOURCE. The energy equation is not labelled an “ISO 9906 formula.”
Published numerical check
The DOE final rule publishes a water test relation in U.S. units using Q = 1,000 U.S. gal/min, H = 100 ft and specific gravity 1.00. Its precise 3956 denominator gives 25.2780586 hp of pump output. Using the equivalent density implied by that published constant, this worksheet’s SI path returns the same value; the check is retained in the independent test artifact. Ordinary tests use directly documented density and gravity rather than a rounded U.S. denominator.
NIST SP 811 Appendix B.8 is the unit-conversion reference. It lists standard acceleration 9.80665 m/s² and conversions for the foot, U.S. gallon per minute, mass density, mechanical horsepower and psi.
| Former content or behavior | Problem and correction |
|---|---|
| Hidden g = 9.81 m/s² | Gravity affects both the physical calculation and U.S. conversion conventions. The replacement requires a documented value and identifies 9.80665 only as conventional standard gravity, never as a prefilled site value. |
| η entered without a defined boundary | “Hydraulic efficiency” can be confused with pump efficiency. The replacement requires ηp = pump output power / pump input power at the same complete-pump boundary. |
| Generic 50–90% efficiency ranges by pump size | Those ranges were not an operating-point source and could silently manufacture input power. They were removed; controlled curve/test provenance is mandatory. |
| “Motor should be rated at least at calculated shaft power” | This was an incomplete motor-selection instruction. It ignored the exact pump/driver boundary, driver efficiency, service/duty, starts, transients, derating and governing rules. The worksheet emits no motor size. |
| “10 m head ≈ 1 bar” without conditions | Pressure equivalence depends on ρ and g, while pump total head also accounts for energy terms. The output now calculates ρgH and labels it pressure-equivalent only. |
| Defaults, presets, auto-calculation, partial parsing and dynamic HTML | These produced authoritative-looking results from example, stale or partially parsed values. The page starts blank, requires provenance and confirmation, validates complete numeric strings and writes results with textContent. |
