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A short reach of a $2$ m wide rectangular open channel has its bed level rising in the direction of flow at a slope of $1$ in $10000$. It carries a discharge of $4 m^3/s$ and its Manning’s roughness coefficient is $0.01$. The flow in this reach is gradually varying. At a certain section in this reach, the depth of flow was measured as $0.5$ m. The rate of change of the water depth with distance, $dy/dx$, at this section is _______ (use $g=10\:m/s^2$).
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