Soil and Water Conservation Engineering · Fluid Mechanics · 1 mark · Numerical answer
A best-hydraulic trapezoidal grassed waterway has side slope1H:1V, Q=1 m³/s, bed slope1% and Manning n=.04. Find design depth in metres, to two decimals.
For optimal trapezoid with side slope z=1,$b=2y(\sqrt2-1)$ and hydraulic radius $R=y/2$. Area is $(b+y)y=(2\sqrt2-1)y^2$. Manning gives $1=(1/.04)(2\sqrt2-1)y^2(y/2)^{2/3}\sqrt{.01}$. Solve to obtain $y=.6725907$ m, rounded **.67 m**.
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