Given that, S0 = slope of the channel bottom, S= slope of the energy line, F = Froude Number, the equation of gradually varied flow is expressed as:

1
\(\frac{{dy}}{{dx}} = \frac{{{S_o} - {S_e}}}{{1 + {F^2}}}\)
2
\(\frac{{dy}}{{dx}} = \frac{{{S_o} - {S_e}}}{{1 - {F^2}}}\)
3
\(\frac{{dy}}{{dx}} = \frac{{{S_o} + {S_e}}}{{1 + {F^2}}}\)
4
\(\frac{{dy}}{{dx}} = \frac{{{S_o} + {S_e}}}{{1 - {F^2}}}\)

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