Leak Detection Pressure Drop Calculator

ANA›Life Services Authority›National Calculator Authority›Leak Detection Pressure Drop Calculator

.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; } }

Leak Detection Pressure Drop Calculator

Calculate the expected pressure drop in a pressurized system over time due to a leak, or determine the leak rate from observed pressure loss. Based on the ideal gas law and orifice flow equations.

Initial Pressure (P₁)

kPa (abs)

System Volume (V)

m³

Gas Temperature (T)

°C

Test Duration (t)

minutes

Final Pressure (P₂) (leave blank to calculate)

kPa (abs)

Leak Orifice Area (A) (leave blank to calculate)

m²

Discharge Coefficient (Cd)

—

Gas Molar Mass (M)

Air (28.97 g/mol) Hydrogen (2.016 g/mol) Methane (16.043 g/mol) CO₂ (44.010 g/mol) Oxygen (31.998 g/mol) Nitrogen (28.014 g/mol) Custom

Custom Molar Mass

g/mol

Atmospheric Pressure (P_atm)

kPa

Heat Capacity Ratio (γ)

—

Calculate

document.getElementById('lea-molar-mass').addEventListener('change', function() { document.getElementById('lea-custom-molar-row').style.display = this.value === 'custom' ? 'flex' : 'none'; });

function leaShowError(msg) { var e = document.getElementById('lea-error'); e.textContent = msg; e.style.display = 'block'; document.getElementById('lea-result').style.display = 'none'; }

function leaCalc() { document.getElementById('lea-error').style.display = 'none'; document.getElementById('lea-result').style.display = 'none';

var P1 = parseFloat(document.getElementById('lea-p1').value); var V = parseFloat(document.getElementById('lea-volume').value); var T_C = parseFloat(document.getElementById('lea-temp').value); var t_min = parseFloat(document.getElementById('lea-time').value); var P2_in = document.getElementById('lea-p2').value.trim(); var A_in = document.getElementById('lea-leak-area').value.trim(); var Cd = parseFloat(document.getElementById('lea-cd').value); var gamma = parseFloat(document.getElementById('lea-gamma').value); var P_atm = parseFloat(document.getElementById('lea-p-atm').value);

var molarSel = document.getElementById('lea-molar-mass').value; var M; if (molarSel === 'custom') { M = parseFloat(document.getElementById('lea-custom-molar').value) / 1000; if (isNaN(M) || M 1) { leaShowError('Discharge coefficient must be between 0 and 1.'); return; } if (isNaN(gamma) || gamma = P1) { leaShowError('Final pressure must be less than initial pressure for a leak to exist.'); return; } if (P2 ' + 'Pressure Drop (ΔP)' + dP.toFixed(3) + ' kPa' + 'Pressure Drop Rate' + dP_rate.toFixed(4) + ' kPa/min' + 'Mass of Gas Lost (Δm)' + (delta_m * 1000).toFixed(4) + ' g' + 'Average Mass Leak Rate' + (Q_m_avg * 1000).toFixed(6) + ' g/s' + 'Volumetric Leak Rate (STP)' + (Q_v_std * 1e6).toFixed(4) + ' cm³/s' + 'Equivalent Orifice Area' + A_equiv.toExponential(4) + ' m²' + 'Equivalent Orifice Diameter' + d_equiv.toFixed(4) + ' mm' + 'Flow Regime (at P₁)' + flowRegime + '' + ''; }

// ── MODE 3: A given, P2 blank → simulate pressure drop numerically ── else if (!hasP2 && hasA) { var A_m2 = parseFloat(A_in); if (isNaN(A_m2) || A_m2 ' + 'Calculated Final Pressure (P₂)' + P2_calc.toFixed(3) + ' kPa' + 'Total Pressure Drop (ΔP)' + dP_total.toFixed(3) + ' kPa' + 'Pressure Drop Rate' + dP_rate.toFixed(4) + ' kPa/min' + 'Orifice Diameter' + d_mm.toFixed(4) + ' mm' + 'Total Mass Lost' + (total_mass_lost * 1000).toFixed(4) + ' g' + 'Average Mass Leak Rate' + (Q_m_avg * 1000).toFixed(6) + ' g/s' + 'Volumetric Leak Rate (STP)' + (Q_v_std * 1e6).toFixed(4) + ' cm³/s' + 'Flow Regime' + flowRegime + '' + ''; }

// ── MODE 1: Both P2 and A given → full analysis ── else { var P2 = parseFloat(P2_in); var A_m2 = parseFloat(A_in); if (isNaN(P2) || P2 = P1) { leaShowError('Final pressure must be less than initial pressure.'); return; } if (P2 ' + 'Pressure Drop (ΔP)' + dP.toFixed(3) + ' kPa' + 'Pressure Drop Rate' + dP_rate.toFixed(4) + ' kPa/min' + 'Orifice Diameter' + d_mm.toFixed(4) + ' mm' + 'Mass Lost (from ΔP)' + (delta_m_obs * 1000).toFixed(4) + ' g' + 'Leak Rate (from ΔP)' + (Q_m_obs * 1000).toFixed(6) + ' g/s' + 'Leak Rate (from orifice, avg P)' + (Q_m_orifice * 1000).toFixed(6) + ' g/s' + 'Vol. Leak Rate — ΔP method (STP)' + (Q_v_obs * 1e6).toFixed(4) + ' cm³/s' + 'Vol. Leak Rate — Orifice method (STP)' + (Q_v_orifice * 1e6).toFixed(4) + ' cm³/s' + 'Flow Regime' + flowRegime + '' + ''; }

var res = document.getElementById('lea-result'); res.innerHTML = html; res.style.display = 'block'; }

#### Formulas Used

1. Ideal Gas Law — Mass of Gas Lost:

Δm = (P₁ − P₂) · V / (R_specific · T) where R_specific = R / M = 8.314 / M  [J/(kg·K)]

2. Average Leak Rate:

Q̇_m = Δm / t  [kg/s]

3. Isentropic Orifice Flow — Choked (sonic) when P_atm/P_up ≤ (2/(γ+1))^(γ/(γ−1)):

Q̇_m = Cd · A · P_up · √(γ·M/(R·T)) · (2/(γ+1))^((γ+1)/(2(γ−1)))

4. Isentropic Orifice Flow — Subsonic:

Q̇_m = Cd · A · P_up · √(M/(R·T)) · √[ 2γ/(γ−1) · ((P_d/P_up)^(2/γ) − (P_d/P_up)^((γ+1)/γ)) ]

5. Volumetric Leak Rate at STP (0 °C, 101.325 kPa):

Q̇_v = Q̇_m · R · T_std / (M · P_std)

6. Numerical Simulation (Mode 3): Euler integration of dP/dt using the orifice equation at each time step, with 10,000 sub-steps for accuracy.

#### Assumptions & References

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References

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