where V is the overall mean velocity across the channel, R is the hydraulic mean depth (see Fig. 7.4), So is the bed slope and C is a coefficient. R is obtained for all required stages from R = A/P with A and P measured in the cross-sectional survey. If C^/So is taken to be constant (k), then Q versus kA^/R plots as a straight line. For gauged stage values of H, corresponding values of A R and Q are obtained and plotted. The extended straight line can then be used to give discharges for higher stages (Fig. 7.25). The method relies on the doubtful assumption of C remaining constant for all stage values.

Fig. 7.25 The Stevens method. The Manning formula

This can be used instead of the Chezy formula for extending rating curves, but it is also applied more widely in engineering practice for calculating flows. The formula, where quantities are in SI units, is,

It is applied in a similar way, with So2 /n assumed constant, and Q being plotted against AR2/3.

In both the Stevens and Manning formula methods, when a flood discharge exceeds bank-full stage, the roughness factor, C or n, can be changed to model the different flow conditions and the separate parts of the extended flow over the flood plain are calculated with the modified formula. It is generally accepted that the Manning equation is superior to the Chezy equation, since n changes less than C as R varies (Fortune et al, 2004).

Estimates of flood discharges at strategic locations along a river are usually made by this Manning-based method. After notable flood events, surveyors can measure the required cross-sectional area, the wetted perimeter and the bed slope of the affected reach; the peak surface water level is assessed from debris or wrack marks. Selecting an appropriate value of n (Table 7.1 or, for greater detail, see BS 3680-5:1992) for the channel roughness, an estimated peak discharge is calculated. Considerable experience is needed in using this method since the validity of the formula depends on the nature of the flow and the appropriate corresponding line of slope. The conveyance and afflux estimation system (CES/AES)

The CES/AES software toolbox1 has been developed recently for application in the UK (Abril and Knight, 2004; Knight et al., 2010). It contains a 'conveyance generator' that can be used to extend rating curves by utilising channel roughness information from 700 UK sources (including the UK River Habitat Survey) together with descriptions of the channel cross-sections and the effects of vegetation growth within the channel. It also makes use of experimental data from UK Flood Channel Facility at the University of Birmingham in allowing for additional momentum losses at boundary between channel and overbank flow.

Within the UK, the Hiflows-UK database holds the rating curve information for approximately 1000 gauging stations.

Table 7.1 Sample values of Manning's n

Concrete-lined channel


Unlined earth channel


Straight, stable deep natural channel


Winding natural streams


Variable rivers, vegetated banks


Mountainous streams, rocky beds


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