Consider the open, rectangular channel flow shown in the figure above. Fluid travels

from left to right across a flat channel bed, while the channel width gradually changes

from $5ft$ to $3ft.$

a$)[2$ point$]$ If the flow rate through the channel is $30f\frac{t^3}{s}$ and the average velocity at

the wide end of the channel is $V_1=1\mathrm{.}5f\frac{t}{s},$ what is the depth of flow, $y_1,$ at the

wide end of the channel?

b$)[2$ points$]$ Is the flow sub$-$critical, super$-$critical, or critical at the left side of the

channel?

c$)[6$ points$]$ If the flow is critical at the narrow end of the channel, use the Bernoulli

equation and the continuity equation to help you calculate the depth of flow, $y_2,$

the velocity of flow, $V_2,$ and the width of the channel, $b_2.$