Valve Authority Explorer — Control Valve Sizing

1 · The circuit (at design flow)

DESIGN FLOW Q_d PUMP DIFFERENTIAL ΔP_total SYSTEM LOSS AT Q_d (pipe + exchanger + orifice) SPECIFIC GRAVITY

2 · The valve you bought

RATED C_v (full open)

RANGEABILITY R TURNDOWN CASE — MIN FLOW

0.50VALVE AUTHORITY N

N = ΔP_valve ÷ ΔP_total (at design flow)

ΔP ACROSS VALVE

REQUIRED C_v / K_v

TRAVEL AT DESIGN

TRAVEL AT MIN FLOW

OVERSIZE FACTOR

INSTALLED GAIN @ DESIGN

Reading the curves. The dashed grey line is the inherent characteristic — what the trim does on a test bench at constant ΔP. The solid steel line is the installed characteristic — the same trim inside this circuit, where opening the valve raises the flow, the system loss grows as Q², and the valve's own ΔP collapses. Low authority bends the installed line up into a quick-opening shape: all the flow change happens in the first 20 % of travel, and the loop has almost no resolution left anywhere above it.

Not modelled: choked flow and flashing. Liquid flow stops obeying Q = K_v√(ΔP/SG) once ΔP exceeds ΔP_choked = F_L²(P₁ − F_F·P_v); past that point more ΔP buys no more flow, only cavitation damage. A pump-curve droop (head falling as flow rises) is also ignored — ΔP_total is held constant here.