Question

Design a riprap-lined trapezoidal channel that has a capacity of 1000 cfs and slope of 0.0005 ft/ft. Crushed rock is to be used and the channel bottom with is not to exceed 15 ft. Determine the riprap size, the side slopes, and the design depth of flow.

Answer 1

Explanation:

assume maximum permissible is 4 ft/s and n=0.025 we have the formula:

$V=\frac{1.49}{n} R_{h} ^2^/^3S_{0} ^1^/^2$

$R_{h} =(Vn/1.49S_{0} ^1^/^2)^3^/^2$

where

$V= 0.0005\\S_{0} =1000cfs$

we get

$R_{h} =((0.0005*0.025/1.49*1000^1^/^2))^3^/^2=1.36 ft$

$A=Q/V=1000cfs/4.00ft/s=250ft^2$

assume side slopes will be 1 vertical to 2 horizontal

$P=A/R_{h} =250ft^2/1.36 ft=183ft$

also

$P=b+2y\sqrt{1+4} =b+2y\sqrt{5} =183ft\\\\A=by+2y^2=250ft^2$

Solve the above two equations for the bottom width b and depth y.