Figure P$6\mathrm{.}31$ shows a side view of a broad crested weir. The symbols shown in Fig. P$6\mathrm{.}31$ are defined as: $H_w=$ the height of the weir $(m),H_h=$ the head above the weir $($m$),$ and $H=H_w+H_h=$ the depth of the river upstream of the weir $(m).$

A broad$-$crested weir used to control depth and velocity of rivers and streams.

The flow across the weir, $Q_w(\frac{m^3}{s}),$ can be computed as $($Munson et al$.,2009)$

$Q_w=C_w{B}_w\sqrt[\phantom{2}]{g}(\frac{2}{3}{)}^{\frac{3}{2}}{H}_h^{\frac{3}{2}}$

where $C_w=$ Weir

Coefficient $($dimensiontess$),$

$B_w=$ weir width $(m)$ and

$g=$ gravitational constant $(\frac{m}{s^2})$

Cw is given as

$C_w=1\mathrm{.}125\sqrt[\phantom{2}]{\frac{1+\frac{H_h}{H_w}}{2+\frac{H_h}{H_w}}}$

Given $g=9\mathrm{.}81\frac{m}{s^2},H_w=0\mathrm{.}8m,$

$B_W=8m$ and $Q_w=1\mathrm{.}3\frac{m^3}{s}.$

Use fzero to obtain the upsitream depth, $H$