Semi-theoretical, Kennedy, Lacey approaches

Semi-theoretical approach

Uses a basic flow formula (Manning's or Chezy's) with empirical limits for non-silting, non-scouring velocity and a chosen $B/D$ ratio (from standards). The section is found from $Q = AV$ and $V = \frac{1}{n}R^{2/3}S^{1/2}$, with $V$ and $B/D$ fixed by experience, and the slope is checked against the allowable value.

Kennedy's approach

Based on the critical velocity concept, $V_0 = 0.55mD^{0.64}$ (vertical eddies from the bed). Kutter's formula gives $V$. Trial and error on $D$ gives the section for a known $S$.

Lacey's approach

Regime theory for alluvial channels with a silt factor $f$; $V$, $R$, $P$ and $S$ come directly from $Q$ and $f$.

Critical comparison

Semi-theoretical designs are the practical choice for canals where silt is not a problem (hill irrigation systems, non-alluvial soils). Kennedy and Lacey apply to alluvial soils, with Lacey's method preferred for new works.