Hot Water Heat Loss Calculator
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.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Hot Water Heat Loss Calculator
Calculate heat loss from hot water pipes or storage tanks based on temperature difference, insulation, and geometry.
System Type
Pipe Storage Tank
Hot Water Temperature (°C)
Ambient Temperature (°C)
Pipe Length (m)
Pipe Inner Diameter (mm)
Pipe Outer Diameter (mm)
Insulation Thickness (mm) (0 = uninsulated)
Insulation Thermal Conductivity (W/m·K)
Tank Volume (litres)
Tank Surface Area (m²) (0 = auto from volume)
Insulation Thickness (mm) (0 = uninsulated)
Insulation Thermal Conductivity (W/m·K)
Inner Surface Heat Transfer Coefficient (W/m²·K)
Outer Surface Heat Transfer Coefficient (W/m²·K)
Pipe/Tank Wall Thermal Conductivity (W/m·K)
Steel ≈ 50, Copper ≈ 385, Plastic ≈ 0.4
Duration (hours)
Calculate Heat Loss Results will appear here.
function hotToggleType() { var t = document.getElementById('hot-system-type').value; document.getElementById('hot-pipe-inputs').style.display = (t === 'pipe') ? '' : 'none'; document.getElementById('hot-tank-inputs').style.display = (t === 'tank') ? '' : 'none'; }
function hotGetVal(id) { return parseFloat(document.getElementById(id).value); }
function hotCalc() { var resultDiv = document.getElementById('hot-result');
var systemType = document.getElementById('hot-system-type').value; var T_hot = hotGetVal('hot-water-temp'); var T_amb = hotGetVal('hot-ambient-temp'); var h_i = hotGetVal('hot-h-inner'); var h_o = hotGetVal('hot-h-outer'); var k_wall = hotGetVal('hot-pipe-k'); var duration = hotGetVal('hot-duration');
// Validation if (isNaN(T_hot) || isNaN(T_amb) || isNaN(h_i) || isNaN(h_o) || isNaN(k_wall) || isNaN(duration)) { resultDiv.innerHTML = 'Please fill in all fields with valid numbers.'; return; } if (T_hot Hot water temperature must be greater than ambient temperature.'; return; } if (h_i Heat transfer coefficients, conductivity, and duration must be positive.'; return; }
var deltaT = T_hot - T_amb; var Q_watts, details, geometry;
if (systemType === 'pipe') { // ---- PIPE: Cylindrical heat loss ---- var L = hotGetVal('hot-pipe-length'); var r1_mm = hotGetVal('hot-pipe-inner-diameter') / 2; var r2_mm = hotGetVal('hot-pipe-outer-diameter') / 2; var ins_mm = hotGetVal('hot-insulation-thickness-pipe'); var k_ins = hotGetVal('hot-insulation-k-pipe');
if (isNaN(L) || isNaN(r1_mm) || isNaN(r2_mm) || isNaN(ins_mm) || isNaN(k_ins)) { resultDiv.innerHTML = 'Please fill in all pipe fields.'; return; } if (r1_mm Outer diameter must be greater than inner diameter, and both must be positive.'; return; } if (L Pipe length must be positive.'; return; } if (ins_mm Insulation thickness must be ≥ 0 and conductivity must be positive.'; return; }
var r1 = r1_mm / 1000; // inner radius (m) var r2 = r2_mm / 1000; // outer radius (m) var r3 = r2 + ins_mm / 1000; // outer insulation radius (m)
// Cylindrical thermal resistance per unit length (m·K/W): // R_total = 1/(h_i * 2π r1 L) + ln(r2/r1)/(2π k_wall L) + ln(r3/r2)/(2π k_ins L) + 1/(h_o * 2π r3 L) var R_conv_inner = 1.0 / (h_i * 2 * Math.PI * r1 * L); var R_wall = Math.log(r2 / r1) / (2 * Math.PI * k_wall * L); var R_ins = (ins_mm > 0) ? Math.log(r3 / r2) / (2 * Math.PI * k_ins * L) : 0; var R_conv_outer = 1.0 / (h_o * 2 * Math.PI * r3 * L); var R_total = R_conv_inner + R_wall + R_ins + R_conv_outer;
Q_watts = deltaT / R_total;
var outerSurface = 2 * Math.PI * r3 * L; geometry = 'Pipe: ' + L.toFixed(1) + ' m long, ID=' + (r1_mm2).toFixed(1) + ' mm, OD=' + (r2_mm2).toFixed(1) + ' mm' + (ins_mm > 0 ? ', Insulation=' + ins_mm.toFixed(0) + ' mm' : ', Uninsulated'); details = 'Inner convection resistance' + R_conv_inner.toFixed(4) + ' K/W' + 'Pipe wall conduction resistance' + R_wall.toFixed(4) + ' K/W' + (ins_mm > 0 ? 'Insulation conduction resistance' + R_ins.toFixed(4) + ' K/W' : '') + 'Outer convection resistance' + R_conv_outer.toFixed(4) + ' K/W' + 'Total thermal resistance' + R_total.toFixed(4) + ' K/W' + 'Outer surface area' + outerSurface.toFixed(3) + ' m²';
} else { // ---- TANK: Flat-wall approximation ---- var V_litres = hotGetVal('hot-tank-volume'); var A_manual = hotGetVal('hot-tank-surface-area'); var ins_mm_t = hotGetVal('hot-insulation-thickness-tank'); var k_ins_t = hotGetVal('hot-insulation-k-tank');
if (isNaN(V_litres) || isNaN(A_manual) || isNaN(ins_mm_t) || isNaN(k_ins_t)) { resultDiv.innerHTML = 'Please fill in all tank fields.'; return; } if (V_litres Tank volume must be positive.'; return; } if (ins_mm_t Insulation thickness must be ≥ 0 and conductivity must be positive.'; return; }
// Auto surface area from volume assuming spherical tank (minimum surface for volume) // For a cylinder with H=D: A = 3 * (π * V)^(2/3) * (4/3)^(-2/3) ... simpler: use sphere // Sphere: V = (4/3)π r³ → r = (3V/4π)^(1/3), A = 4π r² var V_m3 = V_litres / 1000; var A_auto = 4 * Math.PI * Math.pow(3 * V_m3 / (4 * Math.PI), 2/3); var A = (A_manual > 0) ? A_manual : A_auto; var autoNote = (A_manual 0) ? t_ins / (k_ins_t * A) : 0; var R_conv_outer_t = 1.0 / (h_o * A); var R_total_t = R_conv_inner_t + R_wall_t + R_ins_t + R_conv_outer_t;
Q_watts = deltaT / R_total_t;
geometry = 'Tank: ' + V_litres.toFixed(0) + ' L, Surface area=' + A.toFixed(3) + ' m²' + autoNote + (ins_mm_t > 0 ? ', Insulation=' + ins_mm_t.toFixed(0) + ' mm' : ', Uninsulated'); details = 'Surface area used' + A.toFixed(4) + ' m²' + autoNote + '' + 'Inner convection resistance' + R_conv_inner_t.toFixed(6) + ' K/W' + 'Tank wall conduction resistance (5 mm)' + R_wall_t.toFixed(6) + ' K/W' + (ins_mm_t > 0 ? 'Insulation conduction resistance' + R_ins_t.toFixed(6) + ' K/W' : '') + 'Outer convection resistance' + R_conv_outer_t.toFixed(6) + ' K/W' + 'Total thermal resistance' + R_total_t.toFixed(6) + ' K/W'; }
var Q_kW = Q_watts / 1000; var Q_total_kWh = Q_kW * duration; var Q_total_MJ = Q_total_kWh * 3.6;
// Temperature drop in tank (if tank mode) var tempDropNote = ''; if (systemType === 'tank') { var V_litres2 = hotGetVal('hot-tank-volume'); var mass_kg = V_litres2; // water density ≈ 1 kg/L var cp = 4186; // J/(kg·K) var energy_J = Q_total_kWh * 3600 * 1000; var deltaT_drop = energy_J / (mass_kg * cp); tempDropNote = 'Estimated tank temperature drop' + deltaT_drop.toFixed(2) + ' °C over ' + duration.toFixed(1) + ' h'; }
resultDiv.innerHTML = '### Results ' + '' + geometry + '
' + '' + 'ParameterValue' + 'Temperature difference (ΔT)' + deltaT.toFixed(2) + ' °C' + details + 'Heat loss rate' + Q_watts.toFixed(2) + ' W (' + Q_kW.toFixed(4) + ' kW)' + 'Total heat loss over ' + duration.toFixed(1) + ' h' + Q_total_kWh.toFixed(3) + ' kWh (' + Q_total_MJ.toFixed(2) + ' MJ)' + tempDropNote + ''; }
#### Formulas Used
Pipe (Cylindrical Geometry) — Fourier's Law for radial conduction:
Q = ΔT / Rtotal
Rtotal = 1/(hi·2πr₁L) + ln(r₂/r₁)/(2πkwallL) + ln(r₃/r₂)/(2πkinsL) + 1/(ho·2πr₃L)
Where: r₁ = inner radius, r₂ = outer pipe radius, r₃ = outer insulation radius, L = pipe length
Tank (Flat-Wall / Planar Geometry):
Q = ΔT / Rtotal
Rtotal = 1/(hi·A) + twall/(kwall·A) + tins/(kins·A) + 1/(ho·A)
Auto surface area (spherical): A = 4π·(3V/4π)2/3
Tank temperature drop: ΔTdrop = Q·t / (m·cp), where m = mass of water, cp = 4186 J/(kg·K)
Total energy loss: E = Q × t (kWh)
#### Assumptions & References
- Specific heat of water: cp = 4186 J/(kg·K) (Incropera & DeWitt, Fundamentals of Heat and Mass Transfer).
- Inner convective coefficient hi ≈ 300 W/m²·K is typical for turbulent water flow; ho ≈ 10 W/m²·K for natural convection in air.
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