Hydraulic resistance ($R=\Delta p/Q$)

Hydraulic resistance relates the pressure drop across a resistive fluid element to its volumetric flow rate. In a linear model, $\Delta p=RQ$ with $R>0$, so dissipated mechanical power is $\Delta pQ=R{Q}^2$. A peripheral circulatory bed can be represented by such a resistance when its detailed dynamics are not retained. This terminal pressure-to-flow resistance differs from the area-dependent friction rate multiplying velocity in a distributed tube momentum equation.

A network of two resistive rails joined by multiple cross-links. Finite rail resistance makes cross-link flows unequal; maintaining a three-terminal equivalent permits exact recursive reduction.

Replacement of a three-edge triangular linear resistance network by a three-arm star with the same relation between terminal pressures and flows. Each star arm equals the product of its two adjacent triangle edges divided by the sum of all three edges.