Question

For a trapezoidal-shaped, concrete-finished gravel bottom channel along a 0.5% slope, with a bottom width of 8 feet, a top width of 32 feet, and side slopes of 4:1, calculate:
a. the channel’s full capacity discharge,
b. velocity at full capacity discharge, and
c. discharge and velocity when stream flow is 0.5 feet from the top of the channel.

Answer 1

Given,

Trapezoidal shaped concrete finished gravel bottom channel

n = 0.012

Slope = 0.5 % = 0.005

Bottom width = 8 ft

Side slope = 4:1

Top width = B + 4y + 4y = 32 ft

y = 3 ft

Area = 0.5 * y * (B+T) = 0.5 * 3 * 40 = 60

Perimeter = = 32.74 ft

R = A/P = 60/32.74 = 1.833 ft

b) Velocity at full capacity discharge:

= 8.84 ft/sec

a) Channel's full capacity discharge:

Q = A * V = 60 * 8.84 = 530.4 /sec

c) Discharge and velocity when stream flow is 0.5 ft from top of channel

y = 3 - 0.5 = 2.5 ft

T = B + 8y = 8 + 8 * 2.5 = 28 ft

A = 0.5 * 2.5 * 36 = 45

P = = 28.62 ft

R = A/P = 45/28.62 = 1.57 ft

Velocity,

= 7.96 ft/sec

Discharge, Q = A * V = 45 * 7.96 = 358.2 /sec