Water Filter Flow Rate Calculator
Calculate the flow rate through a water filter, estimate pressure drop, and determine filter capacity and replacement schedule based on your filter specifications.
Filter Specifications
Total active filtration area of the filter element Intrinsic permeability of filter media (1 Darcy ≈ 9.869×10⁻¹³ m²)Operating Conditions
Typical household: 275–550 kPa (40–80 psi) Total volume the filter can process before replacement
Results will appear here after calculation.
Formula Used
Darcy's Law for flow through porous media:
Q = (k × A × ΔP) / (μ × L)
- Q — Volumetric flow rate (m³/s)
- k — Intrinsic permeability of filter media (m²); 1 Darcy = 9.869×10⁻¹³ m²
- A — Filter cross-sectional area (m²)
- ΔP — Pressure differential across filter (Pa) = Pin − Pout
- μ — Dynamic viscosity of water (Pa·s), calculated via the Vogel equation: μ = 2.414×10⁻⁵ × 10^(247.8 / (T − 140)) where T is in Kelvin
- L — Filter thickness / depth (m)
Filter lifespan: Days = Rated Capacity (L) / Daily Usage (L/day)
Reynolds number check: Re = ρ × v × d_pore / μ — Darcy's Law assumes Re < 1 (creeping/laminar flow through pores).
Assumptions & References
- Flow is assumed to be laminar and incompressible through the filter media (Darcy flow regime, Re < 1).
- The filter media is assumed to be homogeneous and isotropic with uniform permeability.
- Water is treated as a Newtonian fluid; viscosity varies with temperature using the Vogel equation.
- Permeability preset values are representative estimates; actual values vary by manufacturer and fouling state.
- Reverse osmosis recovery rate is assumed at ~60%; actual recovery depends on membrane type, pressure, and feed water quality.
- Filter lifespan estimate assumes constant daily usage and does not account for fouling-induced flow reduction over time.
- Pore diameter for Reynolds number estimation uses the Kozeny-Carman approximation: d ≈ √(180k), assuming porosity ~0.4.
- References: Bear, J. (1972). Dynamics of Fluids in Porous Media. Elsevier. | Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon. | Vogel, W. (1921). Viscosity-temperature relationship for water.