Classwork A trapezoidal channel with side slopes of 2 to 1 i

Classwork: A trapezoidal channel with side slopes of 2 to 1 is designed to carry a normal flow of 200 cfs. The channel is grass-lined with a Manning\'s n of o.025 and has a bottom slope of 0.0006 ft/ft. Determine the normal depth, bottom width, and top width (see figure below) assuming normal flow and the bottom width (WB) as 1.5 times the normal depth. TW 2 BW 1.5y V1.00 no/ S 495-.5) BW ???0.0006??137,00??4.52???6,78 TW 24,87 0.025 200

Solution

step 1:

Given data:

Q=200 ft³/sec

n=0.025

S=0.0006

B=1.5y

side slope =1:2

step 2:

required parameters:

Top width, bottom width and depth

step 3:

According to mannings equation:

V=(1/n)(R^0.66S^0.5)

Calculate the Hydraulic radius

R=A/P

R=(b+2y)y/(2y[(1+2^2)]^0.5)

R=(1.5y+2y)y/(2y(1+4)^0.5) R=0.78 Y

V=(1/0.025)(0.78Y)^0.66(0.0006)^0.5

step 4:

According to contunity equation

Q=AV

200=(1.5y+2y)y(40)(0.78y)^0.66x0.0244

y= 4.91 feet

B=1.5x4.91

B=7.36 feet

Top width=2y(1+z²)^0.5

T=2x4.91(1+4)^0.5

T=27.005 feet