Static Pressure Drop Calculator for Duct Systems

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Static Pressure Drop Calculator for Duct Systems

Calculate the static pressure drop in HVAC duct systems for both circular and rectangular ducts using the Darcy-Weisbach equation with the Colebrook-White friction factor.

Duct Shape

Circular Rectangular

Duct Diameter (inches)

Duct Width (inches)

Duct Height (inches)

Duct Length (feet)

Airflow Rate (CFM)

Duct Material

Galvanized Steel (smooth) — ε = 0.0003 ft Galvanized Steel (standard) — ε = 0.001 ft Aluminum — ε = 0.0005 ft Flexible Duct (extended) — ε = 0.003 ft Flexible Duct (compressed) — ε = 0.015 ft Fiberglass Duct Board — ε = 0.005 ft Custom Roughness

Custom Absolute Roughness (ft)

Air Temperature (°F)

Altitude (feet above sea level)

Calculate Pressure Drop

#### Formulas Used

Darcy-Weisbach Equation:

ΔP = f × (L / Dh) × (ρ × V²) / 2

Where:

Hydraulic Diameter (rectangular duct):

Dh = (4 × W × H) / (2 × (W + H)) = (2 × W × H) / (W + H)

Colebrook-White Equation (implicit, solved iteratively):

1/√f = −2.0 × log₁₀(ε/(3.7 × Dh) + 2.51/(Re × √f))

Swamee-Jain Explicit Approximation (initial estimate):

f = 0.25 / [log₁₀(ε/(3.7 × Dh) + 5.74/Re⁰·⁹)]²

Reynolds Number:

Re = ρ × V × Dh / μ

Air Density (altitude & temperature corrected):

ρ = 1.2929 × (273.15 / TK) × (Palt / 101325)

Palt = 101325 × (1 − 2.25577×10⁻⁵ × altitude_m)^5.25588

Dynamic Viscosity of Air (Sutherland's Law):

μ = μ₀ × (T/T₀)^(3/2) × (T₀ + S)/(T + S)

where μ₀ = 1.716×10⁻⁵ Pa·s, T₀ = 273.15 K, S = 110.4 K

Pressure drop per 100 ft (common HVAC metric):

ΔP/100ft = ΔP_total × (100 / L_ft)

#### Assumptions & References

(function() {

function staToggleDuctShape() { var shape = document.getElementById('sta-duct-type').value; document.getElementById('sta-circular-inputs').style.display = (shape === 'circular') ? '' : 'none'; document.getElementById('sta-rectangular-inputs').style.display = (shape === 'rectangular') ? '' : 'none'; } window.staToggleDuctShape = staToggleDuctShape;

document.getElementById('sta-roughness').addEventListener('change', function() { var isCustom = this.value === 'custom'; document.getElementById('sta-custom-roughness-group').style.display = isCustom ? '' : 'none'; });

function staGetVal(id) { return parseFloat(document.getElementById(id).value); }

function staShowError(msg) { var el = document.getElementById('sta-result'); el.style.display = 'block'; el.innerHTML = '⚠ ' + msg + ''; }

// Colebrook-White solved via Newton-Raphson iteration function colebrookFriction(Re, relRoughness) { if (Re 200) { staShowError('Air temperature must be between -20°F and 200°F.'); return; } if (isNaN(altitude) || altitude 120) { staShowError('Diameter seems unrealistically large (max 120 inches).'); return; } Dh_ft = diam / 12.0; ductDesc = diam.toFixed(1) + '" diameter circular duct'; } else { var width = staGetVal('sta-width'); var height = staGetVal('sta-height'); if (isNaN(width) || width 120 || height > 120) { staShowError('Duct dimensions seem unrealistically large (max 120 inches each).'); return; } var W_ft = width / 12.0; var H_ft = height / 12.0; Dh_ft = (2.0 * W_ft * H_ft) / (W_ft + H_ft); ductDesc = width.toFixed(1) + '" × ' + height.toFixed(1) + '" rectangular duct (D_h = ' + (Dh_ft * 12).toFixed(2) + '")'; }

// Cross-sectional area in ft² var area_ft2; if (shape === 'circular') { var r = Dh_ft / 2.0; area_ft2 = Math.PI * r * r; } else { var W2 = staGetVal('sta-width') / 12.0; var H2 = staGetVal('sta-height') / 12.0; area_ft2 = W2 * H2; }

// Velocity in ft/min and ft/s var velocity_fpm = airflow / area_ft2; var velocity_fps = velocity_fpm / 60.0;

// Sanity check velocity if (velocity_fpm > 10000) { staShowError('Calculated velocity (' + Math.round(velocity_fpm) + ' FPM) is extremely high. Check inputs — typical HVAC ducts run 400–2500 FPM.'); return; }

// Convert to SI var Dh_m = Dh_ft * 0.3048; var L_m = length * 0.3048; var V_ms = velocity_fps * 0.3048; var roughness_m = roughness_ft * 0.3048;

// Air properties var rho = airDensity(tempF, altitude); // kg/m³ var mu = airViscosity(tempF); // Pa·s

// Reynolds number var Re = rho * V_ms * Dh_m / mu;

// Relative roughness var relRoughness = roughness_m / Dh_m;

// Friction factor var f = colebrookFriction(Re, relRoughness);

// Darcy-Weisbach pressure drop (Pa) var dP_Pa = f * (L_m / Dh_m) * (rho * V_ms * V_ms) / 2.0;

// Convert to in. w.g. (1 Pa = 0.00401463 in. w.g.) var dP_inwg = dP_Pa * 0.00401463;

// Per 100 ft var dP_per100ft = (length > 0) ? dP_inwg * (100.0 / length) : 0;

// Velocity pressure (in. w.g.) var Vp_Pa = 0.5 * rho * V_ms * V_ms; var Vp_inwg = Vp_Pa * 0.00401463;

// Flow regime label var regime; if (Re = 0.06 && dP_per100ft 0.15) { ashrae_msg = '⚠ Above typical ASHRAE range (0.06–0.15 in. w.g./100 ft) — consider larger duct or lower velocity.'; ashrae_color = '#c0392b'; } else { ashrae_msg = '✔ Within ASHRAE recommended range (0.06–0.15 in. w.g./100 ft).'; ashrae_color = '#27ae60'; }

// Density ratio vs standard air var rho_std = 1.2041; // kg/m³ at 68°F, sea level var densityRatio = rho / rho_std;

var html = '### Results ' + '' + 'Duct Configuration' + '' + ductDesc + ''

var el = document.getElementById('sta-result'); el.style.display = 'block'; el.innerHTML = html; } window.staCalc = staCalc;

})();

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References

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