Engineering Sizing Formulas & External Design Tools¶
Practical engineering equations and curated links to the global WASH sector's leading calculation and simulation software.
🌐 Curated Industry-Standard Sizing Calculators & Software¶
Before building custom models, field practitioners should utilize these established, peer-reviewed engineering tools:
1. Solar Photovoltaic Pumping¶
- Grundfos Product Center (GPC) Solar Sizing — Free online tool that sizes SQFlex submersible and surface solar pumps using satellite solar radiation data for any GPS coordinate globally.
- LORENTZ COMPASS Solar Sizing Software — The benchmark software used across Africa and South Asia to simulate solar PV water output, pipe friction, and seasonal drawdown.
2. Piped Distribution Networks & Hydraulics¶
- US EPA EPANET 2.2 — Free, open-source hydraulic and water quality network modeling software for pressurized distribution networks, tanks, and pumping stations.
- HydroCAD Stormwater & Siphon Modeling — Computer-aided design system for modeling drainage, storage ponds, and hydrology.
- Engineering Toolbox Hazen-Williams Online Calculator — Instant in-browser friction head loss calculation for various pipe diameters and materials.
3. Groundwater Drilling & Cost Modeling¶
- Rural Water Supply Network (RWSN) Borehole Costing Tool — Comprehensive spreadsheet model for calculating true CapEx per meter drilled, casing BoQ, and hydrogeological risk contingency across Sub-Saharan Africa.
- Practica Foundation Manual Drilling Toolkits — Technical charts and decision matrices for manual percussion, jetting, and sludging feasibility.
4. Water Filtration & Treatment¶
- CAWST BioSand Design & Sieve Gradation Spreadsheets — Official design tools for sand gradation envelopes, flow rate calibration ($400\text{ mL/min}$), and biological layer maintenance.
- WHO Water Safety Planning (WSP) Risk Matrix — Standardized sanitary inspection spreadsheets and hazard scoring templates.
📐 Field Engineering Sizing Formulas & Governing Equations¶
1. Solar Photovoltaic Water Pumping Sizing¶
Daily Hydraulic Energy Required ($E_h$)¶
$$E_h = \frac{V \times H_{TDH} \times \rho \times g}{3.6 \times 10^6} \quad \text{[kWh/day]}$$
- $V$ = Daily water volume required ($m^3/day$)
- $H_{TDH}$ = Total Dynamic Head ($m$) = Static Lift + Pipe Friction Losses + Delivery Elevation
- $\rho$ = Density of water ($1000 \text{ kg/m}^3$)
- $g$ = Acceleration due to gravity ($9.81 \text{ m/s}^2$)
Required Solar Array Peak Power ($P_{peak}$)¶
$$P_{peak} = \frac{E_h}{\text{PSH} \times \eta_{pump} \times \eta_{mismatch}} \quad \text{[kWp]}$$
- $\text{PSH}$ = Peak Sun Hours per day ($kWh/m^2/day$, typically 4.5 – 6.0 in tropical regions)
- $\eta_{pump}$ = Submersible motor/pump efficiency (typically 0.45 – 0.65)
- $\eta_{mismatch}$ = Dust, temperature, and wiring derating factor (~0.80)
2. Pipe Friction Head Loss (Hazen-Williams Equation)¶
$$h_f = 10.67 \times L \times \frac{Q^{1.852}}{C^{1.852} \times D^{4.87}}$$
- $h_f$ = Friction head loss ($m$)
- $L$ = Total pipe length ($m$)
- $Q$ = Volumetric flow rate ($m^3/s$)
- $D$ = Inside pipe diameter ($m$)
- $C$ = Hazen-Williams roughness coefficient ($C = 140–150$ for smooth PVC/PE pipe)
3. Rooftop Rainwater Harvest Potential¶
$$\text{Annual Yield (Liters)} = A \times R \times C_r \times \eta_f$$
- $A$ = Roof catchment footprint area ($m^2$)
- $R$ = Annual precipitation ($mm$)
- $C_r$ = Runoff coefficient ($0.85$ for corrugated metal, $0.80$ for tile)
- $\eta_f$ = First-flush diverter filter efficiency ($0.90$)
4. Sand Dam Stored Water Capacity¶
$$V_{water} = L_{dam} \times W_{avg} \times D_{avg} \times 0.5 \times \phi_{sand}$$
- $L_{dam}$ = Upstream sand riverbed length ($m$)
- $W_{avg}$ = Average dry riverbed width ($m$)
- $D_{avg}$ = Maximum sand depth at weir ($m$)
- $\phi_{sand}$ = Specific yield / drainable porosity of coarse quartz sand ($0.25–0.40$)