Contents preface (VII) introduction 1—37

8.5.1.3. Lacey’s Method
Lacey (11) stated that the dimensions width, depth, and slope of a regime channel to carry a given water discharge loaded with a given sediment discharge are all fixed by nature. According to him, the fundamental requirements for a channel to be in regime are as follows :
(i) The channel flows uniformly in incoherent alluvium. Incoherent alluvium is the loose granular material which can scour or deposit with the same ease. The material may range from very fine sand to gravel, pebbles, and boulders of small size.
(ii) The characteristics and the discharge of the sediment are constant. (iii) The water discharge in the channel is constant.

The perfect ‘regime’ conditions rarely exist. The channels which have lateral restraint (because of rigid banks) or imposed slope are not considered as regime channels. For example, an artificial channel, excavated with width and longitudinal slope smaller than those required, will tend to widen its width and steepen its slope if the banks and bed are of incoherent alluvium and non-rigid. In case of rigid banks, the width is not widened but the slope becomes steeper. Lacey termed this regime as the initial regime. A channel in initial regime is narrower than it would have been if the banks were not rigid. This channel has attained working stability. If the continued flow of water overcomes the resistance to bank erosion so that the channel now has freedom to adjust its perimeter, slope, and depth in accordance with the discharge, the channel is likely to attain what Lacey termed the final regime.

The river bed material may not be active at low stages of the river particularly if the bed is composed of coarse sand and boulders. However, at higher stages, the bed material becomes active, i.e., it starts moving. As such, it is only during the high stages that the river may achieve regime conditions. This fact is utilised in solving problems related to floods in river channels.

DESIGN OF STABLE CHANNELS

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Lacey also suggested that for a regime channel the roughness coefficient as well as the critical velocity ratio should be dependent on sediment size alone. However, it is now well known that in a movable bed channel, the total roughness includes grain as well as form roughness. Likewise, the non-silting and non-scouring velocity (included in the critical velocity ratio) shall depend on the sediment load and the size of the sediment.

Lacey felt that the sediment in an alluvial channel is kept in suspension by the vertical components of eddies generated at all points along the wetted perimeter. He, therefore, plotted the available data of regime channels to obtain a relationship between the regime velocity U (in m/s) and the hydraulic radius R(in metres). He, thus, found that U ∝ R^1/2 and that the exponential power did not change with data. He, therefore, formulated

U = C′ R

(8.23)

in which C′ is a proportionality constant.

Including a factor f₁ to account for the size and density of sediment, Lacey finally obtained

U =

^2 f R = 0.632