Consider a flow through a sloping rectangular channel

with base $30$ m and height $($depth$)=H(m).$ Using

continuity and Manning equation, the depth of the

channel in terms of flow rate $Q=6\frac{m^3}{s}$ and velocity

$S=0\mathrm{.}0005\frac{m}{s}$ is given by $f(H)=\frac{\frac{s^1}{2}}{n}\frac{(BH{)}^{\frac{3}{3}}}{\frac{(B+2H{)}^2}{3^{?}}}-Q.$ Given the

manning roughness coefficient as $n=0\mathrm{.}03,$ estimate the

depth H of the rectangular flow using False position

method with initial values as $0,1.$