Rework example 5.4.2 using equation (5.4.8), .EXAMPLE 5.4.2For a river section with a subc...

Rework example 5.4.2 using equation (5.4.8), .

EXAMPLE 5.4.2

For a river section with a subcritical discharge of 6500 ft3/s, the water surface elevation at the downstream section is 5710.5 ft with a velocity head of 3.72 ft. The next section is 500 ft upstream with a velocity head of 1.95 ft. The conveyances for the downstream and upstream sections are 76,140 and 104,300, respectively. Using expansion and contraction coefficients of 0.3 and 0.1, respectively, determine the water surface elevation at the upstream section.

SOLUTION

Using equation (5.4.12), the objective is to solve for the upstream water surface elevation w1:

The friction slope term is

Because Δ[α(V2/2g)] > 0, a contraction exists for flow from cross-section 1 to cross-section 2. Then

The water surface elevation at the upstream cross-section is then