The relationship for flow through a valve is
where F is the volumetric flow rate, Cv is the valve coefficient, x is the fraction of valve opening, ΔPv is the pressure drop across the valve, s.g. is the specific gravity of the fluid, and f(x) is the flow characteristic.
Three common valve characteristics are linear, equal-percentage, and quick-opening. For a linear valve,
For an equal-percentage valve,
For a quick-opening valve
The three characteristics are ...