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

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).

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  1. 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

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