Kennedy's theory features and limitations

Kennedy's theory (R.G. Kennedy, 1895, from the Upper Bari Doab canal, Punjab) is for the design of alluvial earthen channels that neither silt nor scour.

Salient features

• Silt is kept in suspension by the vertical components of eddies formed at the channel bed. The channel remains stable when the mean velocity equals the critical velocity $V_0$.
• Critical velocity: $V_0 = 0.55\,m\,D^{0.64}$, $D$ = depth (m), $m$ = critical velocity ratio $V/V_0$ ($m$ = 1.1 for coarse silt, 0.8 for very fine silt, 1.0 for normal).
• The mean velocity in the channel is found from Kutter's formula (or Manning's) with a rugosity coefficient $n$.
• For a given $Q$ and $S$ the section is found by trial and error so that $V = V_0$, with $A = Q/V$.
• Valid for stable channels in alluvium which carry fine silt, with trapezoidal section and side slopes taken from soil types.
• A tabular/graphical (Garret's diagram) solution can be used to reduce the work.

Limitations

1. Considers eddies from the bed only; sides ignored.
2. $m$ is chosen by judgement; there is no relation to the silt grade or the silt charge.
3. A single equation ($V_0$) is used for a design that actually involves several unknowns ($B, D, S$), so the depth and width are not uniquely determined unless $S$ or $B/D$ is assumed.
4. Requires Kutter's $n$, which is not well defined for silt-laden flow.
5. Based on the data of one region (Upper Bari Doab canals), not on fully regime channels.
6. Trial-and-error design; the bed width/depth relation $B/D$ is not controlled, and the ratio can become unreasonable.
7. Does not account for the silt load carried, so cannot be used where the canal carries heavy silt.