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A $3$ m wide rectangular channel carries a flow of $6 \: m^3 /s$. The depth of flow at a section $P$ is $0.5 \: m$. A flat-topped hump is to be placed at the downstream of the section $P$. Assume negligible energy loss between section $P$ and hump, and consider $g$ as $9.81 \: m/s^2$. The maximum height of the hump (expressed in $m$) which will not change the depth of flow at section P is ________
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