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UPPSC AE Civil 2013 Official Paper I

- \(\frac{v}{{\sqrt {gy} }}\)
- \(\frac{{2v}}{{\sqrt {gy} }}\)
- \(\frac{v}{{\sqrt {2gy} }}\)
- \(\frac{v}{{\sqrt {g\left( {\frac{y}{2}} \right)} }}\)

Option 4 : \(\frac{v}{{\sqrt {g\left( {\frac{y}{2}} \right)} }}\)

Froude’s number= \(\frac{{\rm{v}}}{{\sqrt {{\rm{g}} \times \left( {\frac{{\rm{A}}}{{\rm{T}}}} \right)} }}\)

Where,

A = Area of cross-section, and T = Top width

For a triangular channel as stated above

\({{\rm{F}}_{\rm{r}}} = \frac{{\rm{v}}}{{\sqrt {\frac{{{\rm{gA}}}}{{\rm{T}}}} }}\)

T = 2y + 2y = 4y

\({\rm{A}} = \frac{1}{2} \times 4{\rm{y}} \times {\rm{y}} = 2{y^2}\)

\(\therefore {{\rm{F}}_{\rm{r}}} = \frac{{\rm{v}}}{{\sqrt {{\rm{g}} \times \frac{{2{{\rm{y}}^2}}}{{4{\rm{y}}}}} }}\)

\({{\rm{F}}_{\rm{r}}} = \frac{{\rm{v}}}{{\sqrt {{\rm{g}}\left( {\frac{{\rm{y}}}{2}} \right)} }}\)

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