Water Pressure Loss Calculator

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Water Pressure Loss Calculator

Calculate pressure loss (head loss) in pipes using the Darcy-Weisbach equation combined with the Colebrook-White equation for friction factor.

Flow Rate (L/s)

Pipe Internal Diameter (mm)

Pipe Length (m)

Pipe Roughness ε (mm)

-- Select material or enter custom -- Drawn copper / brass (0.0015 mm) Commercial steel (0.046 mm) Asphalted cast iron (0.12 mm) Galvanized iron (0.26 mm) Cast iron (0.9 mm) Concrete (3.0 mm) Smooth (PVC / PE) (0.0 mm)

Water Temperature (°C)

Calculate Results will appear here.

function watSetRoughness() { var sel = document.getElementById('wat-roughness-select'); if (sel.value !== '') { document.getElementById('wat-roughness').value = sel.value; } }

// Kinematic viscosity of water as function of temperature (°C) // Using Vogel-type approximation valid 0–100°C, returns m²/s function watKinematicViscosity(T) { // Dynamic viscosity (Pa·s) via empirical formula (Kestin et al.) var mu = 2.414e-5 * Math.pow(10, 247.8 / (T + 133.15 + 273.15 - 273.15)); // More accurate: use direct table interpolation approximation // μ (Pa·s) = A * 10^(B/(T+C)) — Andrade equation // A=2.414e-5, B=247.8, C=140 (T in °C, offset to Kelvin internally) var muPas = 2.414e-5 * Math.pow(10, 247.8 / (T + 140.0)); // Density of water (kg/m³) — simplified polynomial var rho = 999.842 - 0.0622 * T - 0.00354 * T * T; var nu = muPas / rho; // m²/s return { nu: nu, rho: rho, mu: muPas }; }

// Colebrook-White equation solved iteratively for Darcy friction factor // 1/sqrt(f) = -2 * log10( ε/(3.7D) + 2.51/(Resqrt(f)) ) function watFrictionFactor(Re, relRoughness) { if (Re 100) errors.push('Temperature must be between 0 and 100 °C.');

if (errors.length > 0) { resultDiv.innerHTML = '⚠ ' + errors.join('⚠ ') + ''; return; }

// Unit conversions var Q = Q_ls / 1000.0; // m³/s var D = D_mm / 1000.0; // m var e = eps / 1000.0; // m (absolute roughness)

// Cross-sectional area var A = Math.PI * D * D / 4.0; // m²

// Flow velocity var V = Q / A; // m/s

// Fluid properties var fluid = watKinematicViscosity(T); var nu = fluid.nu; // m²/s var rho = fluid.rho; // kg/m³

// Reynolds number var Re = V * D / nu;

// Relative roughness var relRoughness = e / D;

// Friction factor (Darcy-Weisbach) var f = watFrictionFactor(Re, relRoughness);

// Head loss — Darcy-Weisbach: hf = f * (L/D) * V²/(2g) var g = 9.80665; // m/s² var hf = f * (L / D) * (V * V) / (2.0 * g); // m (metres of water)

// Pressure loss var dP = rho * g * hf; // Pa var dP_kPa = dP / 1000.0; // kPa var dP_bar = dP / 100000.0; // bar var dP_psi = dP / 6894.757; // psi

// Flow regime var regime = Re ' + 'Flow Velocity' + V.toFixed(4) + ' m/s' + 'Reynolds Number' + Re.toFixed(0) + ' (' + regime + ')' + 'Darcy Friction Factor (f)' + f.toFixed(6) + '' + 'Head Loss (hf)' + hf.toFixed(4) + ' m' + 'Pressure Loss' + dP_kPa.toFixed(3) + ' kPa' + 'Pressure Loss' + dP_bar.toFixed(5) + ' bar' + 'Pressure Loss' + dP_psi.toFixed(4) + ' psi' + 'Velocity Head (hv)' + hv.toFixed(5) + ' m' + 'Water Density at ' + T.toFixed(1) + '°C' + rho.toFixed(2) + ' kg/m³' + 'Kinematic Viscosity' + nu.toExponential(4) + ' m²/s' + ''; }

#### Formulas Used

Darcy-Weisbach Equation (head loss):

hf = f · (L / D) · V² / (2g)

where: f = Darcy friction factor, L = pipe length (m), D = internal diameter (m), V = mean flow velocity (m/s), g = 9.80665 m/s²

Flow Velocity: V = Q / A = Q / (π D² / 4)

Reynolds Number: Re = V · D / ν

Colebrook-White Equation (turbulent flow, Re ≥ 4000):

1 / √f = −2 · log₁₀( ε/(3.7·D) + 2.51 / (Re · √f) )

Solved iteratively; initial guess from Swamee-Jain: f = 0.25 / [log₁₀(ε/(3.7D) + 5.74/Re⁰·⁹)]²

Laminar flow (Re < 2300): f = 64 / Re

Pressure Loss: ΔP = ρ · g · hf (Pa)

Kinematic Viscosity (Andrade equation): μ = 2.414×10⁻⁵ · 10^(247.8 / (T + 140)) Pa·s; ν = μ / ρ

#### Assumptions & References

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References

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