Question

A trapezoidal section has a 5.0-ft bed width, 2.5-ft depth, and 1:1 side slope. Evaluate its geometric elements (Area, water depth, wetted perimeter, top width, hydraulic radius, and hydraulic depth).

Answer 1

Answer:

a) 18.75 ft^2

b) 2.5 ft

c) 12.07 ft

d) 10 ft

e) 1.553 ft

f) 1.875 ft

Explanation:

Given data :

5.0-ft bed width, ( b )

2.5-ft depth ( y )

1 : 1 side slope

Evaluate

a) Area of trapezoidal section

A = by + my^2

we assume m = 1

A = [5 + (1 * 2.5 ) ] *2.5

   = ( 7.5 ) 2.5  = 18.75 ft^2

b) Calculate water depth

water depth = 2.5 ft

c) Calculate wetted perimeter

P = b + 2y √ 1 + m^2

  = 5 + (2.5*2) √ 1 + 1 ^2  =   12.07 ft

d) calculate top width

    T = b + 2my

       = 5 + 2 ( 1 * 2.5 ) = 10 ft

e) calculate hydraulic radius

R = A / P = 18.75 / 12.07

               = 1.553 ft

f) calculate hydraulic depth

 D = A / T = 18.75 / 10 = 1.875 ft