Plant Energy Audits, Compressed-Air Systems & Choked Sonic Flow
Compressed-Air Orifice Leak SCFM & Annual kWh Waste Formula
Calculate Sonic Choked Compressed-Air Orifice Leak Flow (SCFM), Continuous Wasted Compressor Power (kW), Annual Electricity Waste (kWh/yr), and Annual Leak Cost ($/yr).
Use absolute pressure (psig + 14.7)—and remember doubling leak diameter quadruples wasted kW!
Above ~13 psig header pressure, compressed air escaping to atmosphere reaches Mach 1 choked sonic velocity at the leak throat! Under the US DOE / CAGI Choked-Orifice Equation at 70°F standard conditions, leak flow is SCFM_leak = 26.6 * C_d * (P_gauge_psig + 14.7) * D_in^2, where C_d (~0.61 for sharp-edged cracks/fittings, ~0.97 for smooth rounded nozzles) is the discharge coefficient! Two mistakes ruin plant ultrasonic leak audits: plugging gauge pressure instead of absolute psia (P_g + 14.7), and forgetting D_in^2—meaning a single 1/4-inch (0.25 in) blown hose fitting leaks 4x as much air as a 1/8-inch (0.125 in) leak and costs over $24,000/yr!
Verify on a 24/7 Automotive Stamping Plant Leak—Header_Gauge_Pressure = 100.0 psig (114.7 psia, B2), Equivalent_Leak_Diameter = 0.25 in (1/4", B3), Sharp_Orifice_Cd = 0.61 (B4), Compressor_Specific_Power = 20.0 kW per 100 SCFM (B5), and Industrial_Electricity_Rate = $0.12/kWh over 8,760 hrs/yr (B6): Choked Leak Flow equals 26.6 * 0.61 * 114.7 * 0.0625 = 116.32 SCFM (E2), Continuous Wasted Shaft Power is 23.26 kW (E3), Annual Wasted Electricity is 203,792.88 kWh/yr (E4), and Annual Leak Cost hits $24,455.15/yr (E5)!
| Ultrasonic Air-Leak Audit KPI (100 psig, 1/4" Sharp Orifice, 20 kW/100 SCFM, $0.12) | Formula | Verified Output |
|---|---|---|
| Choked Sonic Leak Flow (SCFM) | 26.6 * Cd * (Psig + 14.7) * Diam_in^2 | 116.32 SCFM (29.08 @ 1/8") |
| Continuous Wasted Power (kW) | SCFM_Leak * (kW_Per_100SCFM / 100) | 23.26 kW (5.82 kW @ 1/8") |
| Annual Energy Waste (kWh/yr) | Wasted_kW * 8760 | 203,792.88 kWh/yr |
| Annual Leak Electricity Cost ($/yr) | Annual_kWh * Rate_Per_kWh | $24,455.15/yr ($6,113.79 @ 1/8") |
DOE Choked-Orifice SCFM & Annual Leak Cost Formula
Validate Header_psig >= 15 (choked sonic flow threshold!), Diameter_in > 0, Discharge_Cd in (0, 1], Specific_Power > 0, and Electricity_Rate > 0!
=LET(pg_s, B2, dm_i, B3, cd_o, B4, kw_c, B5, el_r, B6, IF(OR(pg_s < 15, dm_i <= 0, cd_o <= 0, cd_o > 1, kw_c <= 0, el_r <= 0), "Invalid Air Leak Input", LET(sc_f, 26.6 * cd_o * (pg_s + 14.7) * (dm_i ^ 2), kw_w, sc_f * (kw_c / 100), ROUND(kw_w * 8760 * el_r, 2))))Quarter-Area 1/8-Inch Orifice Scaling Check (Set Leak Diameter = 0.125 in)
Halve Leak_Orifice_Diam_in B3 from 0.25 in to 0.125 in (1/8"): Leak SCFM E2 drops by exactly 4x to 29.08 SCFM, Wasted Power E3 falls to 5.82 kW, and Annual Cost E5 drops to $6,113.79/yr!
=IF(ISTEXT(E5), E5, ROUND(26.6 * B4 * (B2 + 14.7) * (B3 ^ 2), 2))Try the example
Use the original values or change them to test your understanding.