Air Compressor Size, Receiver Tank and Leak Cost Calculator

Free-air demand follows the load-factor approach in the CAGI Handbook, 7th edition, Chapter 4 (https://www.cagi.org/assets/documents/pdfs/handbook/Chapter_4_handbook_Final2021.pdf?updated=1758723830), printed pp. 1–3: $Q_d=Q_{tools}f(1+a)+Q_{leak}$ and $Q_{required}=\max(Q_d/D_{max},Q_{cutout})$. Here $Q_{cutout}=Q_{tools}f(1+a)+Q_{leak}(p_{high})$. The result is a lower bound: selected delivery must strictly exceed cut-out demand to reach the upper set point. The input volume is delivered during a one-minute reference interval, so the Metric/US volume conversion also expresses m³/min or cfm.

The DOE Sourcebook (2003), printed p. 42 (https://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/compressed_air_sourcebook.pdf) gives isothermal free-air storage $V_f=V\Delta p/p_a$. Applying that balance to a compressor of delivery $Q_c$ gives loaded fraction $D=Q_d/Q_c$, charge time $V_f/(Q_c-Q_d)$ and discharge time $V_f/Q_d$. Solving their sum for a target cycle period gives

For an isolated peak burst starting at cut-out, $V_{burst}=p_a Q_{peak}t_b/\Delta p$, with no compressor credit. Select at least $\max(V_{cycle},V_{burst})$. These are separate scenarios, not a time-varying burst simulation.

Leak mass flow is $\dot m=N C_d A p_u\Psi/\sqrt{RT}$. The sonic factor is $\Psi=\sqrt{k}[2/(k+1)]^{(k+1)/[2(k-1)]}$ when $p_a/p_u\leq[2/(k+1)]^{k/(k-1)}$; the subcritical branch follows the isentropic pressure relation. This is derived from NASA Glenn's compressible mass-flow equation (https://www.grc.nasa.gov/WWW/k-12/airplane/mflchk.html), not an incompressible orifice approximation. Free-air flow is $\dot m/\rho_{ref}$.

DOE Tip Sheet #3 (August 2004), pp. 1–2 (https://www.energy.gov/sites/prod/files/2014/05/f16/compressed_air3.pdf) supplies the opening-shape guidance and the leak-energy cost method. Package specific power is entered electrical input divided by selected FAD. Annual cost is leak flow × specific power × pressurized hours × tariff.

The leak-cost sweep is restricted to diameters for which total mean demand is no greater than permitted loaded capacity and total cut-out demand is strictly below compressor delivery. Diameter limits follow the square-root of available flow because orifice flow scales with diameter squared; infeasible points are omitted.

• Dry ideal air: $k=1.4$ and $R=287.05$ J/(kg·K), treated as constant. Air in the tank, the inlet and the free-air reference share the entered temperature.
• The compressor supplies its stated FAD whenever loaded and no receiver inflow when unloaded. Control delay, sump blowdown, unload power and start transients are excluded from the pressure animation.
• Useful-air load factor and growth allowance are user estimates. Leakage is continuous while pressurized and is evaluated at the arithmetic mean gauge pressure; that constant estimate is used during both cycle segments and the burst.
• The peak event uses all connected tools with the growth allowance, plus the same leak estimate. It begins at cut-out and has no compressor supply. It is assessed independently of the steady cycling case.
• All counted leaks have the same equivalent diameter and discharge coefficient, vent directly to atmosphere, and do not interact.
• The tariff default of 0.12 currency units/kWh is an editable illustration, not a quoted regional price. Enter the current rate from your bill; cost is in that same currency. No tariff database or dated regulatory rule is implemented.

For preliminary sizing of a single fixed-delivery compressor under two-state load/unload or start/stop control, with positive design demand and compressor delivery strictly greater than useful design demand plus leakage evaluated at cut-out pressure. If that condition fails, cyclic result cards and pressure traces are suppressed. Pressure entries must satisfy cut-out > cut-in and cut-out ≤ receiver MAWP at service temperature. The selected tank must meet the larger cycle/burst requirement; a small tank triggers a sizing message.

The pressure sawtooth is an isothermal, constant-demand approximation. The cut-out reachability check uses actual cut-out leakage, while cycle timing remains an approximation using mean-pressure leakage. Timing can be inaccurate close to the recharge-capacity limit. Wide pressure bands make its constant mean-pressure leakage less representative; very rapid discharge can cool the receiver and reduce available storage. This is not a variable-speed, multiple-compressor, piping-loss, dryer-capacity or relief-valve model. A minimum complete cycle does not independently guarantee a manufacturer's minimum loaded time, unloaded time or permitted motor starts; inspect the calculated segment times.

The orifice equation supports sonic and subcritical discharge, but equivalent leak size and coefficient often dominate the uncertainty. DOE's approximate leakage table does not specify its temperature/free-air basis. The 20 °C physical model predicts about 3.1% more flow than its 100 psig table row; reference comparisons allow 5%, without fitting constants to the table. Repair savings may be smaller than attributed leak energy unless compressor controls reduce electrical consumption.

The diameter-sweep endpoint is constrained by the selected compressor's available capacity and allowed duty fraction. It is not a forecast that this compressor can hold the pressure band with arbitrarily large leaks. If useful demand alone exceeds either limit, no feasible leak-cost curve is shown.

The nameplate check certifies no vessel or installation.