In a triangular channel having a side slope of 2 horizontal : 1 vertical, the Froude number is given by

Question

Question

This question was previously asked in

BPSC AE Paper 6 (Civil) 14 Oct 2022 Official Paper

Answer 1

Explanation:

Froude's Number is given by

Fr= \(\frac{{\rm{v}}}{{\sqrt {{\rm{g}} \times \left( {\frac{{\rm{A}}}{{\rm{T}}}} \right)} }}\)

Where,

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

For a triangular channel as stated above

F1 Neel Madhu 30.03.20 D2

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

T = 2y + 2y = 4y

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

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

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