In a $4m$ wide rectangular asphalt channel, a hydraulic jump occurs

where the channel slope changes. The upstream slope is $\frac{3}{100},$

and the downstream slope is $\frac{h}{1000}.$ The upstream depth and

velocity are $0\mathrm{.}5m$ and $8\frac{m}{s},$ respectively. The downstream flow is

uniform, and the velocity in the channel can be calculated using

the Manning equation:

$V=\frac{K}{n}{R}_h^{\frac{2}{3}}{S}_0^{\frac{1}{2}}$

where:

$K=1(SI$ unit$),K=1\mathrm{.}49(BG$ unit$)$

$n=0\mathrm{.}016($asphalt$)$

$R_h=$ hydraulic radius

$S_0=$ slope

$($a$)$ Calculate the depth of flow downstream of the hydraulic jump.

$(5$ points$)$

$($b$)$ Determine the value of $h.(5$ points$)$