Control Valve Authority (Beta)
How much control a modulating valve actually has over its branch flow: authority (beta) = the valve's pressure drop fully OPEN / the total drop across the VARIABLE branch it modulates (valve + coil + variable piping). A 5 psi valve in series with a 3 psi coil is beta = 5/8 = 0.625. A valve only realizes its inherent (equal-percentage/linear) characteristic if it keeps most of the branch drop; a LOW-authority (oversized) valve dropping little while a fixed coil drops most distorts the installed characteristic into an on/off curve that hunts. Target beta >= 0.5 (near-linear), 0.25-0.5 tolerable, < 0.25 poor -- the fix is a SMALLER (lower-Cv) valve, which is why control valves are undersized vs line size. Separate from the Cv flow-capacity sizing (valve-flow-coefficient). A design/commissioning check; the design pressures, valve trim, and engineer/balancer govern.
Formula and source
valve_authority (beta) = valve_pressure_drop_psi / (valve_pressure_drop_psi + controlled_circuit_drop_psi). Target beta >= 0.5; 0.25-0.5 tolerable; < 0.25 poor.
Control valve authority (beta) for the installed valve characteristic (ASHRAE Systems; control-valve manufacturer guidance, Belimo / Honeywell), by name; the design pressures, valve trim, and the engineer / balancer govern.
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