QUESTION $5[18$ Marks$]$

Water flows at a rate of $40\frac{m^3}{s}$ in a trapezoidal channel $($Fig$.$ Q$5)$ with bottom width of $5$ m and side slope of $1$:$2(V$:$H).$ The initial flow depth is $0\mathrm{.}6$ m $.$ Both channels are infinitely long and has similar properties with the conveyance factor $600$ and median particle size of $2\mathrm{.}5$ mm $.$ Assume no head loss due to friction.

Calcurate:

a$)$ Normal depth and velocity

b$)$ Critical flow: depth and velocity

c$)$ Normal and critical bed slopes

d$)$ Specific energy and sequent depth

e$)$ Reynold and Froude numbers and state their status

f$)$ Calculate the following if hydraulic jump will occur.

i$.$ Downstream flow depth

ii$.$ Energy loss in the channel

iii. Velocity downstream of the hydraulic jump

iv$.$ Location, the height and the length of jump

g$)$ Determine and sketch the type of the water surface profile in these channels for a flow depth of $0\mathrm{.}3$ m $.$ Indicate the position of control points and hydraulic jump.