A horizontal open channel of constant rectangular cross section conveys $\backslash (20\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash )$ of fluid. At one point in the channel there is a right angled bend formed by circular arcs, the inner radius being $5$ m and the other $8$ m $.$ In the straight portion of the channel the uniform depth of fluid is $2$ m $.$ Assuming a perfect fluid with constant specific energy of flow and a free vortex flow around the bend, estimate the depth of flow at the inner and outer radii of the bend.

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$(1\mathrm{.}552\backslash$mathrm$\{$~m$\},2\mathrm{.}17\backslash$mathrm$\{$~m$\})$

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