Tools › Fluids and Heat Transfer › Pumps and Fans › Compressed Air System Sizing › Example
100 hp two-compressor shop at 100 psig: demand, leaks, capacity at altitude, receiver, loop header, condensate and the year's energy (DOE Sourcebook methods)
| Tool | Compressed Air System Sizing |
| Source | U.S. Department of Energy and Compressed Air Challenge (2016). Improving Compressed Air System Performance: A Sourcebook for Industry, 3rd ed. DOE/EE-1340 (Fact Sheets 3, 4, 5, 6, 7, 12); U.S. Department of Energy (2004). Energy Tips: Compressed Air, Tip Sheets 1, 3, 6 and 14; U.S. Department of Defense (2022). UFC 3-420-02, Appendix A-4; Harris, E. G. (1917). Compressed Air: Theory and Computations, 2nd ed., eq. (28a) and its worked example. |
| Level | Professional |
Problem
A shop at 1,000 ft, 90 °F and 60 % relative humidity runs blow guns, impact wrenches, die grinders, spray guns, machine actuators, a blast cabinet and a process air line (seven rows of free air while running, units installed, duty cycle, units at the peak and required pressure) with a 10 % leak share, from two 50 hp load / unload rotary screws of 250 cfm and 18 kW per 100 cfm at a 100 psig load set point (110 unload, 95 minimum header), a 160 ft³ receiver, a 250 ft loop header of 3.068 in inside diameter with 40 ft of fittings, three branches, an aftercooler at 100 °F, a refrigerated dryer at a 38 °F pressure dew point drawing 0.79 kW per 100 cfm with 5 psi of treatment drop, 4,000 h a year at $0.10/kWh. Find the average, peak and connected demand, the leak flow, the standard air the compressors deliver at the site and how they share the load, the receiver for a 1-minute peak event, the header and branch drops and velocities against 20 and 30 ft/s and 1 psi per 100 ft, the condensate at the aftercooler and the dryer, the atmospheric dew point of the dried air, and the year's energy, cost, leak cost and the saving of a 10 psi pressure reduction.
Inputs to Enter
- Site 1,000 ft, 90 °F, 60 % RH; standard air 14.696 psia, 68 °F, dry
- Demand rows (flow cfm / units / duty % / at peak / psig): blow guns 10 / 6 / 15 / 3 / 90; impact wrenches 25 / 4 / 25 / 3 / 90; die grinders 20 / 3 / 40 / 2 / 90; spray guns 15 / 2 / 60 / 2 / 50; machine actuators 30 / 4 / 50 / 4 / 80; blast cabinet 80 / 1 / 50 / 1 / 90; process air 200 / 1 / 90 / 1 / 80; leak share 10 % of the supply; 10 leaks of 1/16 in at C_d 0.61
- Compressors C1 and C2: 50 hp, 250 cfm at 100 psig, load / unload, 18 kW per 100 cfm; set points 100 / 110 / 95 psig; event 1 min at the peak; receiver 160 ft³; rule 2 gal per cfm
- Loop header 250 ft, ID 3.068 in, fittings 40 ft, steel, limit 20 ft/s, target 1 psi per 100 ft; branches 40 ft × 1.049 in × 60 cfm, 60 ft × 1.049 in × 30 cfm, 30 ft × 2.067 in × 200 cfm (10 / 10 / 15 ft of fittings, 30 ft/s); aftercooler 100 °F, PDP 38 °F, treatment drop 5 psi, dryer 0.79 kW per 100 cfm; 4,000 h, $0.10/kWh, 30 % unregulated, 10 psi reduction
Answers
- Demand: average 356 scfm, peak 575 scfm, connected 650 scfm; load factor 0.619, diversity 0.885; highest required pressure 90 psig; leaks 39.6 scfm (10 % of the 395.6 scfm supply), peak supply 614.6 scfm; the 10 counted 1/16-in leaks pass 38.7 scfm of free air by the sonic-orifice equation (Tip Sheet 3 table 6.31 cfm each at C_d 1)
- Site: p_a = 14.17 psia; k_std = (p_a − φ p_vs)/p_std × T_std/T_a = 0.8984, so each 250 cfm compressor delivers 224.6 scfm (449.2 installed); C1 base-loaded 45.0 kW, C2 trims at f = 0.761 drawing 45 (0.30 + 0.70 × 0.761) = 37.5 kW; total 82.5 kW, 20.85 kW per 100 scfm
- Pressure budget: 90 + 0.43 (branch) + 0.12 (header) + 5 (treatment) = 95.6 psig required, 4.4 psi under the 100 psig load set point
- Receiver (Fact Sheet 6): V = T (C − S) p_a/(p_1 − p_2) = 1 × (614.6 − 449.2) × 14.17/(110 − 95) = 156.2 ft³ (1,169 gal); the installed 160 ft³ ends the 1-min event at 95.35 psig and pumps back up in 3.16 min with the 53.6 scfm surplus; the 2 gal per cfm rule gives 120 ft³
- Loop header leg (307 scfm, 125 ft + 20 ft): velocity 13.4 ft/s, Re 230,000, f = 0.0197, isothermal Darcy–Weisbach drop 0.121 psi (incompressible 0.121; Harris 0.130; Fritzsche 0.113) against a 1.45 psi target; branches 0.426 / 0.159 / 0.122 psi at 22.4 / 11.2 / 19.2 ft/s
- Moisture: 1,784 lb/h of dry air carrying 18.96 g/kg (dew point 74.2 °F); aftercooler at 100 °F and 114.2 psia saturates at 5.22 g/kg, condensing 588 lb (70.5 gal) per day; the dryer takes the air to 0.614 g/kg, another 197 lb (23.6 gal) per day; a 38 °F pressure dew point is −5.3 °F at atmospheric pressure
- Energy: 82.5 + 3.1 (dryer) = 85.6 kW; 342,400 kWh and $34,240.67 a year; the leaks cost $3,299 a year at the system specific power; a 10 psi reduction saves 8 % (1 % per 2 psi plus 2 % × 30 % unregulated) = $2,639 a year
Notes
The tool's default inputs are this shop; press Submit. The case is illustrative (stated on the page); every method is checked by test_compressed_air_sizing.php against the DOE tip-sheet and Sourcebook examples (Tip Sheet 1 $51,064, Tip Sheet 2 $102,600, Tip Sheet 3 line items, Fact Sheet 12 $54,820 and $68,222, Tip Sheets 6 and 14), Harris's 1917 worked example (18.8 and 7.10 psi), the CAGI loss table reprinted by ORNL and a numpy / scipy script in References/Compressed-Air/checks/ (solve_ivp of the isothermal pipe and receiver equations, 20 seeded systems).