Predicting Biosand Filter Output
Biosand filters are intermittent-flow household water treatment devices that remove pathogens and turbidity through a biological layer atop fine sand. Knowing the expected flow rate helps users size the filter for family needs and schedule daily filling cycles. This calculator applies Darcy’s law, which governs laminar flow through porous media, to approximate how quickly water will percolate through the sand bed under gravity.
Darcy’s law expresses volumetric flow rate \(Q\) as \(Q = k A (\Delta h / L)\), where \(k\) is hydraulic conductivity, \(A\) is cross-sectional area, \(\Delta h\) is hydraulic head, and \(L\) is media depth. For round filters, \(A = \pi (d/2)^2\) with diameter in meters. Hydraulic head is the water level above the sand surface, converted from centimeters to meters. Sand depth becomes \(L\) in meters. The script estimates \(k\) using the Hazen approximation \(k = 0.001 d_{10}^2\) with effective grain size \(d_{10}\) in millimeters. This approximation suits uniform sands commonly used in biosand filters.
Once the flow in cubic meters per second is computed, the calculator converts to liters per hour by multiplying by 3,600, offering an accessible unit for household planning. For instance, a 30 cm diameter filter with 50 cm of sand, a 10 cm water head, and 0.3 mm effective size yields approximately 10 liters per hour. This rate permits a family to produce 40 liters of safe water by refilling the filter four times per day.
The choice of sand influences performance significantly. Smaller grains provide more surface area for biological activity but slow the flow. Larger grains accelerate flow yet may not remove fine particles effectively. The table below illustrates how varying grain size affects hydraulic conductivity using the Hazen equation.
| d10 (mm) | k (m/s) |
|---|---|
| 0.15 | 0.000023 |
| 0.25 | 0.000063 |
| 0.35 | 0.000123 |
| 0.45 | 0.000203 |
These values demonstrate the tradeoff between filtration and throughput. Designers often select 0.15–0.35 mm sand to balance pathogen removal with reasonable flow. The biological layer, known as the schmutzdecke, develops over weeks of use and further slows flow; periodic maintenance such as "swirl and dump" restores performance. Calculating expected flow helps operators recognize deviations that might indicate clogging or poor biological development.
Hydraulic head also plays a role. Filling the filter higher increases pressure and flow, but exceeding about 12 cm can disturb the biological layer. Many designs incorporate a diffuser plate to prevent scouring. The head term \(\Delta h\) in Darcy’s law simply quantifies the driving force. In MathML, the full expression implemented in the script is:
where \(d\) is diameter, \(h\) head, and \(L\) depth. All dimensions are converted to meters to keep units consistent.
While the calculator simplifies complex interactions, it provides a solid baseline. Actual flow may vary due to sand gradation, biological activity, and temperature-dependent viscosity. Nonetheless, estimating flow assists in ensuring the filter meets daily demand. Designers can adjust diameter or sand depth to tailor output. A larger diameter drastically increases area and thus flow, whereas deeper sand slightly reduces flow but improves treatment. Because biosand filters are often constructed from repurposed containers or concrete forms, understanding these relationships aids community organizations and DIY builders in producing effective, reliable systems.
Biosand filtration exemplifies appropriate technology: it employs local materials, requires no electricity, and dramatically improves water quality. By quantifying flow with simple equations, practitioners can better plan deployments, monitor performance, and educate users. Accurate expectations prevent disappointment and encourage consistent use, ultimately enhancing public health in off-grid and developing contexts.