Water Filter Flow Rate Calculator

ANA›Life Services Authority›National Calculator Authority›Water Filter Flow Rate Calculator

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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

Filter Type

Sediment Filter Carbon Block Filter Reverse Osmosis Membrane Ceramic Filter Custom / Other

Filter Surface Area (cm²)

Total active filtration area of the filter element

Filter Thickness / Depth (cm)

Filter Permeability (Darcy)

Intrinsic permeability of filter media (1 Darcy ≈ 9.869×10⁻¹³ m²)

### Operating Conditions

Inlet Pressure (kPa)

Typical household: 275–550 kPa (40–80 psi)

Outlet Pressure (kPa)

Water Temperature (°C)

Filter Rated Capacity (litres)

Total volume the filter can process before replacement

Daily Water Usage (litres/day)

Calculate Flow Rate

Results will appear here after calculation.

function watUpdateFields() { const type = document.getElementById('wat-filter-type').value; const presets = { sediment: { area: 600, thickness: 12, permeability: 0.05, capacity: 15000 }, carbon: { area: 450, thickness: 15, permeability: 0.008, capacity: 10000 }, ro: { area: 370, thickness: 0.2,permeability: 0.0001, capacity: 5000 }, ceramic: { area: 300, thickness: 8, permeability: 0.002, capacity: 20000 }, custom: { area: '', thickness: '', permeability: '', capacity: '' } }; const p = presets[type]; if (p.area !== '') { document.getElementById('wat-filter-area').value = p.area; document.getElementById('wat-filter-thickness').value = p.thickness; document.getElementById('wat-permeability').value = p.permeability; document.getElementById('wat-filter-capacity').value = p.capacity; } else { document.getElementById('wat-filter-area').value = ''; document.getElementById('wat-filter-thickness').value = ''; document.getElementById('wat-permeability').value = ''; document.getElementById('wat-filter-capacity').value = ''; } }

function watCalc() { const resultDiv = document.getElementById('wat-result');

// --- Gather inputs --- const A_cm2 = parseFloat(document.getElementById('wat-filter-area').value); const L_cm = parseFloat(document.getElementById('wat-filter-thickness').value); const k_darcy = parseFloat(document.getElementById('wat-permeability').value); const P_in_kPa = parseFloat(document.getElementById('wat-inlet-pressure').value); const P_out_kPa = parseFloat(document.getElementById('wat-outlet-pressure').value); const T_C = parseFloat(document.getElementById('wat-water-temp').value); const cap_L = parseFloat(document.getElementById('wat-filter-capacity').value); const usage_Lpd = parseFloat(document.getElementById('wat-daily-usage').value);

// --- Validation --- const errors = []; if (isNaN(A_cm2) || A_cm2 = P_in_kPa) errors.push("Inlet pressure must be greater than outlet pressure."); if (isNaN(T_C) || T_C 100) errors.push("Water temperature must be between 0°C and 100°C."); if (isNaN(cap_L) || cap_L 0) { resultDiv.innerHTML = 'Please fix the following:' + errors.map(e => '').join('') + ''; return; }

// ============================================================ // DARCY'S LAW FOR FLOW THROUGH POROUS MEDIA // Q = (k × A × ΔP) / (μ × L) // // Where: // k = permeability [m²] (1 Darcy = 9.869233×10⁻¹³ m²) // A = cross-sectional area [m²] // ΔP = pressure differential [Pa] // μ = dynamic viscosity of water [Pa·s] // L = filter thickness [m] // Q = volumetric flow rate [m³/s] // ============================================================

// Unit conversions const k_m2 = k_darcy * 9.869233e-13; // Darcy → m² const A_m2 = A_cm2 * 1e-4; // cm² → m² const L_m = L_cm * 1e-2; // cm → m const dP_Pa = (P_in_kPa - P_out_kPa) * 1000; // kPa → Pa

// Dynamic viscosity of water (Vogel equation approximation) // μ(T) = A × 10^(B / (T - C)) [Pa·s] // Constants: A=2.414×10⁻⁵, B=247.8, C=140 (T in Kelvin) const T_K = T_C + 273.15; const mu = 2.414e-5 * Math.pow(10, 247.8 / (T_K - 140)); // Pa·s

// Darcy's Law: Q [m³/s] const Q_m3s = (k_m2 * A_m2 * dP_Pa) / (mu * L_m);

// Convert to useful units const Q_Lpm = Q_m3s * 1000 * 60; // litres per minute const Q_Lph = Q_Lpm * 60; // litres per hour const Q_Lpd = Q_Lph * 24; // litres per day (theoretical max)

// Pressure drop (same as ΔP since we computed from it) const dP_kPa = P_in_kPa - P_out_kPa; const dP_psi = dP_kPa * 0.14504;

// Filter velocity (superficial / Darcy velocity) [m/s] const v_ms = Q_m3s / A_m2; // m/s const v_cmm = v_ms * 100 * 60; // cm/min

// Reynolds number (to check laminar flow assumption) // Re = ρ × v × d_pore / μ — approximate pore diameter from permeability // d_pore ≈ sqrt(180 × k) (Kozeny-Carman approximation for porosity ~0.4) const rho = 1000 - 0.003 * (T_C - 4) * (T_C - 4); // kg/m³ (approx) const d_pore = Math.sqrt(180 * k_m2); // m const Re = (rho * v_ms * d_pore) / mu;

// Filter lifespan const lifespan_days = cap_L / usage_Lpd; const lifespan_months = lifespan_days / 30.44;

// Time to fill 1 litre at calculated flow rate const time_1L_s = 1 / (Q_m3s * 1000); // seconds const time_1L_m = time_1L_s / 60; // minutes

// Efficiency note: RO membranes typically 50–75% recovery const filterType = document.getElementById('wat-filter-type').value; let recoveryNote = ''; if (filterType === 'ro') { const recovery = 0.60; // typical 60% const wasteFlow = Q_Lpm * (1 - recovery) / recovery; recoveryNote = **RO Recovery Rate**~60% (typical) **Estimated Waste Water**${wasteFlow.toFixed(3)} L/min **Net Permeate Flow**${(Q_Lpm * recovery).toFixed(3)} L/min; }

// Laminar flow warning let flowWarning = ''; if (Re > 1) { flowWarning = ⚠️ Reynolds number (Re = ${Re.toExponential(2)}) suggests flow may not be fully laminar. Darcy's Law is most accurate for Re < 1. Results are approximate.; }

// Format result resultDiv.innerHTML = ` ${flowWarning} ### Flow Rate Results

ParameterValue Flow Rate${Q_Lpm.toFixed(4)} L/min Flow Rate (L/hr)${Q_Lph.toFixed(3)} L/hr Flow Rate (m³/s)${Q_m3s.toExponential(4)} m³/s Time to fill 1 litre${time_1L_s ${recoveryNote}

### Pressure & Flow Conditions

ParameterValue Pressure Drop (ΔP)${dP_kPa.toFixed(1)} kPa (${dP_psi.toFixed(1)} psi) Water Temperature${T_C}°C Dynamic Viscosity (μ)${(mu * 1000).toFixed(4)} mPa·s Water Density (ρ)${rho.toFixed(1)} kg/m³ Superficial Velocity${v_cmm.toFixed(4)} cm/min Reynolds Number (Re)${Re.toExponential(3)} ${Re

### Filter Lifespan Estimate

ParameterValue Filter Rated Capacity${cap_L.toLocaleString()} litres Your Daily Usage${usage_Lpd.toLocaleString()} L/day Estimated Filter Life${lifespan_days.toFixed(0)} days (~${lifespan_months.toFixed(1)} months) Recommended Replacement${lifespan_months

`; }

// Initialise with sediment filter defaults on load watUpdateFields();

#### Formula Used

Darcy's Law for flow through porous media:

Q = (k × A × ΔP) / (μ × L)

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

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References

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