Practice Problems Mathcad

PROBLEM $1$: As a hydraulic engineer you will be working in the design of an open channel to carry irrigation water. The Manning equation is used to relate the flowrate in the channel with the channel slope and the water depth in the channel. This equation can be written for a rectangular open channel as

$Q=\frac{\sqrt[\phantom{2}]{S}(yb{)}^{\frac{5}{3}}}{n(b+2y{)}^{\frac{2}{3}}}$

where $Q=$ flowrate $(\frac{m^3}{s}),S=$ slope $(\frac{m}{m}),$

$y=$ water depth $(m),b=$ channel width $(m),$ and

$n=$ the Manning roughness coefficient.

Knowing that the channel slope is $S=0\mathrm{.}002,$ the width is $b=10,$ and $n=0\mathrm{.}03,$ use a solve block in Mathcad to determine the water depth $y$ for a flowrate $Q=5\frac{m^3}{s}.$