Air compressibility calculator
Fan output power is only proportional to Q × Pt if air behaves as an incompressible fluid. Above roughly 2.5 kPa that assumption starts to cost you real accuracy. Enter the duty point and get the AMCA 210 compressibility coefficient Kp, the corrected output power, and — if you need it — the iterative conversion to a new density or speed.
Why Q × Pt isn't the whole story
Fan output power would be exactly proportional to airflow times pressure if air were incompressible. It isn't — a fan raises the pressure of the air passing through it, and at higher pressure rises the density change through the fan itself becomes large enough to matter. AMCA 210 corrects for this with a compressibility coefficient, Kp:
x = Pt / (Pt1 + pb)
z = [(γ−1)/γ] × (Hi/Q) / (Pt1 + pb)
Kp = [ln(1+x)/x] / [ln(1+z)/z]
Ho = Q × Pt × Kp
γ is the isentropic exponent of air, 1.4 per AMCA 210 §7.8.2. As pressure drops toward zero, x and z both go to zero and Kp goes to exactly 1 — the familiar incompressible case. The correction grows with pressure: at 500 Pa it's under 1%; by 15 kPa it's approaching 6%.
The 2.5 kPa line
AMCA 210 doesn't leave "does this matter?" to judgement — Section 8.2.1 requires barometric pressure to be listed on any test report once fan pressure exceeds 2.5 kPa (10 in. wg), precisely because compressibility stops being negligible past that point. This calculator uses the same line.
Converting to a new density or speed
Section 7.9 covers converting a measured duty point to a different air density or fan speed. If the new density is within 10% of the test density and the new speed within 5% (Section 7.9.1), Kp can be held constant. Outside those limits, the standard requires an iterative solution (Section 7.9.2) — the corrected Kpc depends on the corrected values themselves. This calculator runs that iteration until Kpc converges, which AMCA 210 notes usually takes two or three passes.