Kennedy and Lacey silt theories compared

Kennedy's silt theory (1895)

Kennedy studied channels of the Upper Bari Doab canal system in Punjab (India) that were in regime. He stated that silt is kept in suspension by the vertical eddies generated at the bed by the flowing water. The upward component of these eddies balances the weight of the silt. Hence there is a critical velocity $V_0$ at which the channel neither silts nor scours:

$$V_0 = 0.55\,m\,D^{0.64}$$

where $D$ = depth of water (m) and $m$ = critical velocity ratio $V/V_0$ (depends on silt grade). The mean velocity $V$ is found with Kutter's (or Manning's) formula. A channel is designed by trial so that $V = V_0$; for a given $Q$ and $S$ the depth, width and velocity are fixed.

Lacey's regime theory (1929-1935)

Lacey said that a channel is in true regime only if it flows uniformly in unlimited incoherent alluvium of the same grade as it carries, and its section, slope and velocity all adjust themselves. Silt is held in suspension by the vertical components of eddies generated at all points of the wetted perimeter (bed and sides), and the section tends to be semi-elliptical. Using a silt factor $f = 1.76\sqrt{d_{mm}}$, he gave:

$$V = \left(\frac{Qf^2}{140}\right)^{1/6},\quad R = \frac{5V^2}{2f},\quad P = 4.75\sqrt{Q},\quad S = \frac{f^{5/3}}{3340\,Q^{1/6}}$$

For a given $Q$ and $f$, every dimension is fixed with no trial and error.

Comparison

Why Lacey's theory is superior

• It considers eddies from the entire wetted perimeter, which is closer to real flow.
• Silt size enters through $f$, so grain size is accounted for directly; Kennedy's $m$ is chosen by judgement.
• It gives the slope as an output, and treats $S$, $P$, $R$, $V$ as depending only on $Q$ and $f$, so the design is quick and unique.
• It does not need a roughness coefficient, which is hard to estimate.
• It defines regime clearly (initial regime, final regime and true regime) and gives a direct relation between the section and the discharge ($P \propto \sqrt Q$).
• Its regime relations are based on data from many canals and rivers in different countries, so they apply better outside Punjab.

Both are empirical and restricted to alluvial channels carrying fine silt. Lacey's equations give only the regime perimeter and do not indicate the section shape directly, which is the main criticism of his method.