Compressed-Air Compression Power (Isentropic) and Energy Cost
The horsepower and running cost to make a given airflow, from first principles: the single-stage adiabatic (isentropic) work hp = 0.004364 x P1 x Q x (k/(k-1)) x [(P2/P1)^((k-1)/k) - 1] with k = 1.4, divided by the overall wire-to-air efficiency and priced over the run hours. It tells a tech whether a 100 cfm demand needs a 20 or 25 hp compressor and how much more a higher discharge pressure draws (100 cfm at 100 psig is ~18 hp; the same at 125 psig climbs 13 percent). Multi-staging with intercooling beats single stage above ~100 psig. A sizing and cost estimate, not a compressor selection.
Formula and source
p2_abs = discharge_psig + 14.7; theo_hp = 0.004364 x inlet_psia x free_air_cfm x (k/(k-1)) x ((p2_abs/inlet_psia)^((k-1)/k) - 1); input_kw = theo_hp x 0.746 / overall_eff; annual_kwh = input_kw x run_hours; annual_cost = annual_kwh x rate_kwh. (k = 1.4)
The standard single-stage adiabatic (isentropic) compression power (hp = 0.004364 x P1 x Q x (k/(k-1)) x [(P2/P1)^((k-1)/k) - 1], P in psia, Q in cfm free air, k = 1.4), by name; the 0.004364 = 144/33,000 unit constant and 0.746 kW/hp are named.
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