P-V Diagram Analysis

A P-V (pressure-volume) diagram shows the relationship between cylinder pressure and volume throughout the compression cycle, including suction, compression, discharge, and expansion strokes. The area enclosed by the curve equals the indicated work per cycle.

P-V diagrams reveal compressor indicated work, volumetric efficiency, and compression exponent, and help identify performance issues such as valve leaks, late valve action, ring blow-by, and pulsation effects.

Adiabatic (isentropic) compression assumes no heat exchange and uses the gas specific heat ratio k. Polytropic compression accounts for real-world heat transfer with an empirical exponent n (typically 1.25 to 1.35 for natural gas), which produces a slightly flatter curve and a more accurate prediction of measured indicator-card behavior.

Clearance gas trapped at top dead center re-expands as the piston reverses, reducing the volume available for fresh suction gas. Volumetric efficiency drops as VE = 1 − c·(r^1/n − 1), where c is the clearance fraction and r is the compression ratio. Larger clearance shifts point 4 farther right on the P-V diagram and lowers VE.

Indicated horsepower equals the area enclosed by the P-V loop multiplied by speed. For a theoretical cycle: IHP = W_cycle · RPM / 33,000, where W_cycle = (n/(n−1))·P_s·(V₁−V₄)·[r^(n−1)/n − 1] in ft-lbf per cycle. Brake horsepower then includes mechanical efficiency: BHP = IHP / η_mech, with η_mech typically 0.93–0.97.