Question

What is the hydraulic radius of ditch, with a cross sectional shape that can be approximated by a triangle, as shown in the figure, if the water height is such that the triangle is equilateral, with a water height of 3 ft? Give your answer in ft.

Answer 1

Since the channel is said to be equilateral triangle, the apex angle would be 60o . The formula to find hydraulic radius is R=(A/P) where A is the cross sectional area of flow and P is the wetted perimeter.

The height of equilateral triangle is 3 feet.

Assume the side of triangle as 's'.

s=sqrt(32+(s/2)2)

Solving this, we get s=3.464 feet

For an equilateral triangle, the area is

Substituting s=3.464 feet, we get A=5.195 ft2

Wetted perimeter, P= 2*h*sec(x/2), where h is the height and x is the apex angle

Here, P= 2*3*sec(60/2)=6.928 ft

Therefore hydraulic radius, R= A/P= 5.195/6.928=0.75 ft