https://orcid.org/0000-0002-8843-211X
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ABSTRACT
A model for stage–discharge relationship in two-stage wide meandering channels, devised by statistical analysis of new experimental boundary shear data and some published shear data, is presented. By evaluating the measured boundary shear percentage on floodplains of unequal length on either side along with corresponding wetted area percentage for sinuous channels, it is seen that different but particular empirical relationships exist between shear percentage and percentage flow area due to various flow mechanisms occurring on floodplains lying on either side of the bend. The empirical relationships obtained for left floodplain shear is an exponential function while that for total floodplain is a power function. Expressions for average zonal velocity and hence for zonal discharge are then estimated by 1D analysis to compute the H–Q rating curve for such channels. This method is validated through its application to different published data sets with discharge prediction error lying close to ±10% on most occasions. The method when compared with some other well-known 1D approaches is found to perform reasonably well as evident from error analysis. The method when tested for predicting flow distribution, the error percentage is again within 10% for available limited data series.
Notations
| α | = | Width ratio |
| β | = | Relative depth or depth ratio |
| δ | = | Ratio of bottom width and depth of main channel |
| ρ | = | Density of flowing liquid |
| g | = | Acceleration due to gravity |
| λ | = | Wavelength of the sine curve |
| τ | = | Point boundary shear stress |
| τz | = | Average shear stress in any zone |
| γ | = | Ratio of floodplain roughness to main channel roughness |
| A | = | Area of compound section |
| %Az | = | zonal percentage area |
| Amc | = | Area of main channel |
| Afp | = | Area of flood plain |
| %Afp | = | Percentage of flood plain area |
| %Amc | = | Percentage of main channel area |
| B | = | Total width of compound section |
| b | = | Bottom width of main channel |
| C | = | Chezy’s channel coefficient |
| d | = | External diameter of the Preston tube |
| fmc | = | Average Darcy’s friction factor in main channel |
| ffp | = | Average Darcy’s friction factor in floodplains |
| fz | = | Zonal friction factor |
| Fr | = | Froude’s number of the flow |
| h | = | Height of main channel up to floodplain bed |
| H | = | Total depth of flow in compound channel |
| nmc | = | Average Manning’s roughness in main channel |
| nfp | = | Average Manning’s roughness in floodplains |
| n | = | Manning’s roughness factor |
| P | = | Wetted perimeter of the compound channel section |
| Pmc | = | Wetted perimeter of the main channel |
| Pfp | = | Wetted perimeter of the floodplain |
| Qcal | = | Calculated or estimated discharge in compound section |
| Qact | = | Actual discharge passing in compound section |
| Qmc | = | Component discharge in main channel |
| Qfp | = | Component discharge in floodplains |
| R | = | Hydraulic mean radius of the channel cross section (A/P) |
| Re | = | Reynod's number of the flow |
| rm | = | radius of the meander |
| R2 | = | Coefficient of determination |
| Sfp | = | Shear force per unit length carried by floodplains |
| Smc | = | Shear force per unit length carried by main channel |
| Pfp | = | Floodplain wetted perimeter |
| S’fp | = | Percentage of ratio of shear force per unit length carried by the floodplains to the total shear force per unit length carried by the whole compound section |
| S’lfp | = | Percentage shear in left floodplain |
| S’mc | = | Percentage of ratio of shear force per unit length carried by the main channel to the total shear force per unit length carried by the whole compound section |
| S’z | = | Zonal boundary shear percentage |
| S | = | Bed slope |
| s | = | Main channel side slope |
| Sr | = | Sinuosity of main channel |
| S’fp | = | Shear force percentages carried by the floodplain perimeter |
| S’mc | = | Shear force percentages carried by the main channel perimeter |
| Umc | = | Average stream-wise velocity in main channel |
| Ufp | = | Average streamwise velocity in floodplain |
| Ulfp | = | Velocity in left floodplain |
| Urfp | = | Velocity in right floodplain |
| Umc | = | Mean velocities of the main channel |
| Ufp | = | Mean velocities of the flood plains |
| Uz | = | The average zonal velocity |
Disclosure statement
No potential conflict of interest was reported by the authors.
