The flow coefficient compresses a valve’s entire internal geometry into a single measurable number. Cv is defined as the US gallons per minute of 60 °F water that pass the valve at exactly a 1 psi pressure drop; its European twin Kv counts m³/h of water at a 1 bar drop, and converting both the flow and pressure units gives Kv = 0.865·Cv — the factor published in the Emerson Control Valve Handbook and implicit in the IEC 60534-2-1 constants. With the coefficient in hand, liquid sizing reduces to Cv = Q·√(SG/ΔP).
The worked pattern is symmetric: a duty of 100 gpm of water with 4 psi allocated to the valve requires Cv = 100 × √(1/4) = 50, and the same Cv 50 valve at a 9 psi drop passes 150 gpm, because flow grows with the square root of the pressure drop. The ΔP that goes in is the drop across the valve alone at sizing flow — never the whole system’s losses — and practical selection targets a rated Cv about 1.25–1.6× the requirement so the valve modulates at 60–80% opening rather than running pinned.
The classic equation carries a scope warning: it is the ISA/IEC liquid equation’s turbulent, non-flashing, non-cavitating simplification. Flashing, cavitation, viscous (low-Reynolds) service, or reducers around the valve all require the full ISA-75.01.01 procedure with the FL, FR, and Fp factors, and gas or steam sizing uses different compressible-flow equations entirely.