Let depth be y and b=2y. Then area $(b+zy)y=4y^2$,wetted perimeter $P=b+2y\sqrt{1+z^2}=(2+2\sqrt5)y$,and hydraulic radius $R=4y/(2+2\sqrt5)$. Manning gives $20=(1/.01)(4y^2)R^{2/3}\sqrt{1/400}$. Solving yields approximately **1.13 m**. All cross-section dimensions scale with y, so Q is proportional to $y^{8/3}$.
More Environmental Hydraulics questions
GATE 2023 ES Q53– A 314 kN plunger balances oil of specific gravity.9 in a 1.5 m diameter vessel. A 1.5 cm…
GATE 2023 ES Q57– An oil pipeline must carry20 L/s under laminar conditions. Kinematic viscosity6×10⁻⁶ m²/s…
GATE 2022 ES Q20– Centrifugal-pump connections are shown. Solid arrow denotes suction and dotted arrow…
GATE 2022 ES Q58– A water venturimeter and mercury differential manometer are shown. Mercury SG13.6,water…
GATE 2022 ES Q59– Reservoirs differ10 m in level and connect through 50 m of .10 m pipe, friction factor…
GATE 2022 ES Q60– A hydraulically efficient rectangular channel has Manning n=1/80,slope .01 and discharge64…