Pump Station & System Head Curve
Operating Point & Power Analysis
Duty Point
Operating Flow Qop
0.0 L/s
Duty Point
Operating Head Hop
0.0 m
Pump Efficiency η
0.0 %
Required Power P
0.0 kW
(Water / Shaft Power)
Hydraulic System Schematic
System Head vs Pump Performance Curve
Reference Data Table
| Flow (L/s) | Pump Head (m) | Efficiency (%) | System Head (m) |
|---|
Operating Point Hydraulics
| Pipe Velocity (v) | 0.00 m/s |
| Reynolds No (Re) | 0 |
| Friction Factor (f) | 0.0000 |
| Friction Head (Hf) | 0.00 m |
| Minor Head (Hm) | 0.00 m |
| Total Dyn. Head (Hsys) | 0.00 m |
Theory & Methodology
1. System Head Curve ($H_{sys}$)
The total head the pump must overcome is the sum of the static lift, pipe friction, and minor losses. The required head grows quadratically with flow rate.
$$H_{sys} = H_{stat} + H_{friction} + H_{minor}$$
2. Darcy-Weisbach Friction ($H_f$)
The most rigorous method for pipe friction, factoring in fluid viscosity and flow turbulence (Reynolds number).
$$H_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g} \quad ; \quad H_m = \Sigma K \cdot \frac{v^2}{2g}$$
3. Swamee-Jain Friction Factor ($f$)
An explicit approximation of the Colebrook-White equation for turbulent flow, dependent on relative pipe roughness ($\epsilon/D$).
$$f = \frac{0.25}{\left[ \log_{10}\left( \frac{\epsilon}{3.7D} + \frac{5.74}{Re^{0.9}} \right) \right]^2}$$
4. Pump Power ($P$)
The actual mechanical power required at the pump shaft, accounting for hydraulic and mechanical inefficiencies ($\eta$).
$$P = \frac{\rho \cdot g \cdot Q \cdot H_{op}}{\eta}$$
Metric: $P(kW) = \frac{9.81 \cdot Q(m^3/s) \cdot H(m)}{\eta}$
Imperial: $P(HP) = \frac{Q(GPM) \cdot H(ft)}{3960 \cdot \eta}$
5. Numerical Methodology & Assumptions
The system-pump duty point is determined using piecewise linear interpolation of the provided pump performance curve combined with the bisection method. The algorithm iteratively narrows the flow range to find the exact intersection where $H_{pump} = H_{sys}$. Standard fluid properties are assumed (kinematic viscosity of water at 20°C: $1.004 \times 10^{-6} \text{ m}^2/\text{s}$).
References
- Colebrook, C. F. (1939). Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. Journal of the Institution of Civil Engineers, 11(4), 133-156. https://doi.org/10.1680/ijoti.1939.13150
- Darcy, H. (1857). Recherches expérimentales relatives au mouvement de l'eau dans les tuyaux. Mallet-Bachelier. Archive at Gallica BnF
- Munson, B. R., Young, D. F., & Okiishi, T. H. (2006). Fundamentals of fluid mechanics (5th ed.). John Wiley & Sons. Google Scholar
- Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, 102(5), 657-664. https://doi.org/10.1061/JYCEAJ.0004542
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