End depth in steeply sloping rough rectangular channels

8 Subhasish Dey
Table 1. Comparison of experimental data of Rajaratnam et al (1976) with computational data
obtained from present analysis.
q " h c h e
~h e
~h e 1=^Q 1=^Q
(m 2 =s) (mm) (m) (m) ^S ~" ^" e (O) (C) (O) (C)
0.048 11.9 0.062 0.037 1.12 0.174 0.290 0.599 0.699 0.085 0.091
0.144 11.9 0.128 0.087 1.43 0.084 0.123 0.683 0.695 0.028 0.025
0.143 11.9 0.128 0.086 2.86 0.084 0.126 0.668 0.637 0.028 0.023
0.119 11.9 0.113 0.074 2.74 0.095 0.145 0.654 0.642 0.034 0.028
0.081 11.9 0.087 0.055 2.51 0.123 0.196 0.627 0.650 0.050 0.045
0.107 11.9 0.104 0.067 2.66 0.103 0.159 0.646 0.645 0.038 0.033
0.064 13.9 0.075 0.048 1.65 0.183 0.286 0.639 0.685 0.080 0.086
0.142 13.9 0.127 0.084 1.97 0.108 0.164 0.657 0.673 0.036 0.037
0.229 13.9 0.175 0.115 2.18 0.078 0.119 0.657 0.665 0.023 0.023
0.223 13.9 0.172 0.107 3.62 0.080 0.129 0.621 0.609 0.023 0.022
0.084 13.9 0.089 0.054 2.91 0.154 0.265 0.604 0.634 0.061 0.065
0.148 13.9 0.130 0.079 3.31 0.105 0.189 0.555 0.620 0.035 0.040
0.040 13.9 0.054 0.032 2.77 0.253 0.425 0.595 0.639 0.130 0.141
0.033 13.9 0.048 0.027 2.66 0.283 0.517 0.547 0.642 0.154 0.191
O ± observed; C ± computed.
with increase in ~" for lower ^S. Figure 3 presents the computed non-dimensional free surface
profiles for F 2 o ˆ 2 (i.e. ^S ˆ 1:87) and different values of ~". The dependency of 1=^Q on ^" e
for different values of ^S is presented in figure 4. The experimental data of Rajaratnam et al
(1976), summarized in table 1, agree satisfactorily with the computed results for most of
the runs. However, for some higher values of ^" e , ~h e differs significantly. This is probably
experimental scatter.
7. Concluding remarks
The free overfall in steeply sloping rectangular channels (rough and wide) has been
theoretically modelled to compute the end-depth ratio (EDR) and the flow profile. An autorecursive
search scheme has been evolved for solving the developed implicit equations
simultaneously. A method has also been presented to estimate the discharge from the
known end depth and Nikuradse equivalent sand roughness. The computational results
compare satisfactorily with the experimental observations.
The author is grateful to Bimalundu Dey for his helpful suggestions during the preparation
of the manuscript.
References
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