Water flows in a $25-ft-$wide rectangular channel with a flowrate of $Q=90f\frac{t^3}{s}$ and an upstream depth of $y_1=0\mathrm{.}45ft$ as shown in

the figure below. Determine the flow depth and the surface elevation at section $(2).$

Concepts

Bernoulli's equation applies along a streamline to frictionless flow

Volume flowrate is constant for steady, incompressible flow

There are two possible depths when the flow area changes in an open channel

Determine the energy of the flow at section $2$

$($a$)$ What is the total energy of the flow at section $2?$

$($b$)$ Using the equation solver on your calculator or a "trial and success" procedure, what are the two physically possible solutions

for the depth $y_2?$ Enter the smaller value first.

and

$($c$)$ What is the critical depth for this flow?

d$)$ What is the Froude number at section $2$ for a depth of $0\mathrm{.}619705ft?$

e$)$ Based on the energy diagram of Figure E$10\mathrm{.}7,$ is it physically possible for the flow to go from a depth of $0\mathrm{.}45ft$ to $0\mathrm{.}619705ft$ in

a frictionless manner with the channel as shown?

f$)$ What is the Froude number at section $2$ for a depth of $0\mathrm{.}88941ft?$

g$)$ Based on the energy diagram of Figure E$10\mathrm{.}7,$ is it physically possible for the flow to go from a depth of $0\mathrm{.}45ft$ to $0\mathrm{.}88941ft$ in

a frictionless manner with the channel as shown?

h$)$ What is the physically possible depth of the water at section $2$ after the ramp?

i$)$ What is the elevation of the surface at section $2?$