Biosand Filter Flow Rate Calculator

How the biosand flow rate is calculated

The calculator applies Darcy’s law, which describes laminar flow through porous media such as sand. In plain language, Darcy’s law says that flow rate increases when the media is more permeable, when the cross-sectional area is larger, when the driving head is higher, and when the flow path is shorter.

In symbols, the volumetric flow rate is written as:

• = volumetric flow rate (m³/s)
• = hydraulic conductivity of the sand (m/s)
• = cross-sectional area of the filter (m²)
• = hydraulic head across the sand layer (m)
• = depth of the sand layer (m)

For a round (cylindrical) biosand filter, the area is:

where is the internal diameter of the filter in meters.

Estimating sand hydraulic conductivity with the Hazen equation

Hydraulic conductivity depends strongly on the sand type and grain size. Rather than measuring it directly, many water and geotechnical engineers use Hazen’s empirical equation for clean, uniformly graded sands. In this calculator, is estimated as:

where is the effective grain size in millimetres (mm). The constant is a simplified coefficient chosen to keep results in a realistic range for biosand filter media; published Hazen coefficients vary depending on units and sand characteristics.

Combined working formula

Substituting the area equation and the Hazen expression for into Darcy’s law gives the form actually implemented in the calculator:

where:

• = filter diameter (m)
• = hydraulic head above the sand surface (m)
• = sand depth (m)
• = effective sand size (mm)

Internally, the calculator converts your centimeter and millimetre inputs to meters to match Darcy’s law units. Once is computed in cubic meters per second (m³/s), it is converted to liters per hour (L/h) using:

This gives an output that is easy to relate to daily water needs.

Interpreting your results

Most household biosand filters are designed to serve a small family. A common planning guideline is on the order of 40–80 liters per day for drinking, cooking, and basic hygiene, depending on climate and local practice. Flow rates are often in the range of 0.3–1.5 liters per minute (roughly 18–90 L/h) after the filter has matured.

When you use the calculator, consider the following interpretations:

• Very low flows (< 20 L/h) – The filter may not provide enough water for a family unless it is refilled many times per day. Extremely low flow can also indicate overly fine sand, excessive headloss due to clogging, or construction problems.
• Moderate flows (20–80 L/h) – This is often a reasonable range for a single biosand filter serving one household, especially where storage containers are used to collect treated water over the day.
• Very high flows (> 100 L/h) – High flow may look attractive but can indicate sand that is too coarse or a bed that is too shallow, which may compromise pathogen removal and turbidity reduction.

It is important to remember that the calculator reflects an idealized hydraulic model. Actual flow will generally be lower than the initial estimate as the biological layer develops and as fine particles accumulate in the sand.

Worked example: estimating daily output

Suppose you are designing a biosand filter for a family of five and want to know whether your planned dimensions will supply enough water.

Design inputs:

• Filter diameter = 30 cm
• Sand depth = 50 cm
• Hydraulic head above sand = 10 cm
• Effective sand size = 0.30 mm

Step by step, the calculator will:

1. Convert dimensions to meters: 30 cm → 0.30 m, 50 cm → 0.50 m, 10 cm → 0.10 m.
2. Compute hydraulic conductivity using Hazen: m/s.
3. Compute cross-sectional area: m².
4. Compute Darcy flux term: .
5. Estimate flow rate in m³/s: m³/s.
6. Convert to L/h: L/h.

In this example, the predicted flow is about 5 liters per hour, which is lower than many practitioners would target. At that rate, even running the filter for many hours per day may not meet the family’s needs. You might respond by increasing the filter diameter, reducing sand depth slightly (while staying within recommended design ranges), or using a slightly coarser sand that still meets treatment guidelines.

By adjusting the inputs in the calculator, you can quickly see how each change affects the estimated output and choose a combination that offers both adequate flow and good treatment potential.

Effect of sand size and other parameters

Three main design variables strongly influence the calculated flow rate:

• Filter diameter – Larger diameter increases cross-sectional area and therefore increases flow roughly in proportion to the square of the diameter.
• Sand depth – Deeper sand increases the flow path length and reduces flow. However, sufficient depth is crucial for pathogen removal and turbidity reduction.
• Hydraulic head – A higher water level above the sand increases the driving force and thus increases flow, up to practical limits where the biological layer might be disturbed.
• Effective sand size – Coarser sand (higher ) has higher hydraulic conductivity and gives higher flow, but may remove pathogens and fine particles less effectively than finer sand.

The simplified Hazen equation captures how conductivity rises as grain size increases. The approximate values below illustrate the trend used in the calculator’s hydraulic conductivity estimate.

Many biosand filter programs choose sand in the range of about 0.15–0.35 mm effective size, aiming for a balance between practical flow rate and good water quality. The calculator allows you to explore this tradeoff numerically, but final sand selection should also follow recognized biosand design standards or program guidelines.

Using the calculator for household planning

To use the calculator in a planning context:

1. Estimate your household’s daily treated water requirement (for example, 8–15 L/person/day for drinking and cooking, plus any additional needs).
2. Enter your proposed filter diameter, sand depth, head, and effective sand size into the calculator.
3. Note the predicted flow in liters per hour and multiply by the number of hours per day you realistically expect the filter to be in use.
4. Compare the predicted daily production to your target requirement.
5. If daily production is too low or too high, adjust the design parameters within recommended biosand guidelines (for example, modestly increasing diameter or optimizing head) and recalculate.

Because actual performance changes as the filter matures and as maintenance is performed, it is wise to build in a safety margin rather than designing to just meet the minimum theoretical requirement.

Assumptions and limitations

The flow estimates from this tool are based on simplified hydraulic theory and should be treated as approximations, not guarantees. Key assumptions and limitations include:

• Laminar flow and Darcy’s law applicability – Darcy’s law assumes laminar flow through a saturated porous medium. At very high gradients or with unusual media, this assumption may not hold, leading to deviations from the calculated flow.
• Uniform, clean sand – The Hazen equation is intended for relatively clean, uniformly graded sands. Natural or locally sourced sands with fines, organic matter, or mixed grain sizes may behave quite differently.
• Ideal construction – The model assumes a well-constructed filter with even flow distribution, no major short-circuiting, and correct layering. Construction defects, cracks, or poor underdrain design can significantly alter performance.
• Biological layer effects – As the schmutzdecke develops, it increases headloss and reduces flow, especially in the first weeks of operation. The calculator does not explicitly model time-dependent biological growth.
• Clogging and maintenance – Fine sediments or infrequent maintenance can clog the upper sand layer and reduce flow. Procedures such as the “swirl and dump” method restore some capacity, but their impact is not represented in the calculation.
• Water temperature and viscosity – Hydraulic conductivity changes slightly with water temperature and viscosity. The calculator assumes typical ambient temperatures and does not adjust for seasonal variations.
• Head definition – The input head is treated as the static water level above the sand. In practice, the effective head changes during a filtration cycle as the water level drops.
• No guarantee of potability – A higher flow rate from this calculator does not imply that the water meets any specific health-based standard. Flow is only one factor in treatment performance.

Because of these limitations, use the calculator as a design and teaching aid, not as a substitute for field testing, pilot filters, or water quality verification.

Safety, standards, and responsible use

This calculator does not test or certify water safety. Even if your design appears hydraulically sound, treated water quality depends on correct filter construction, appropriate sand preparation, consistent operation, and regular maintenance.

For responsible deployment of biosand filters:

• Follow recognized biosand filter construction and operation manuals from reputable organizations.
• Where possible, test treated water against national or WHO-aligned drinking water quality guidelines.
• Train users in correct operation (e.g., pause period, avoiding disturbance of the biological layer, and cleaning methods).
• Monitor performance over time and be prepared to retrofit or replace filters that do not maintain adequate flow or water quality.

Flow rate estimation is one useful design input, but public health outcomes ultimately depend on the combination of hydraulic performance, microbiological removal, and user behavior.