Soil and Water Conservation Engineering · Fluid Mechanics · 2 marks · Numerical answer
Rectangular channels A and B join into rectangular channel C. All have the same lining material, bottom slope and flow depth 2 m. Bottom widths of A and B are 2 m and 1 m. Find C’s bottom width in metres, to two decimals.
For common Manning $n$ and slope, discharge is proportional to conveyance $AR^{2/3}$. At depth 2 m, a width $b$ gives $A=2b$ and $R=2b/(b+4)$. Continuity requires $$2b\left(\frac{2b}{b+4}\right)^{2/3}=4(4/6)^{2/3}+2(2/5)^{2/3}.$$ The right side is approximately 4.13834. Solving the monotone equation gives $b\approx2.47491$ m, rounded **2.47 m**. Simply adding widths would ignore the changed wetted perimeter.
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