Wetted Perimeter

Cross Sectional Area

The volumetric flow rate is given by Q = AV where the flow velocity can be determined from the Manning equation

The next step is to determine the hydraulic radius (R = A/P) by computing the cross sectional area A and the wetted perimeter P.

The angle θ is first calculated:

      θ = cos^-1(0.3d/0.5d) = 53.1^o

The wetted perimeter P is given by

     P = πd - 2(53.1^o/360^o)πd = 2.215d

The cross sectional area A is determined as follows:

     A = πd²/4 - A_I + A_II

where
     A_I = 2(53.1^o/360^o)(πd²/4) = 0.221d²
      A_II = 2(0.3d)(0.3d tan 53.1^o)/2 = 0.120d²

which gives A = 0.684d²

The hydraulic radius thus becomes
    R = A/P = 0.684d²/2.215d = 0.309d

The diameter of the pipe can then be determined from the volumetric flow rate as follows:

    

Hence, a pipe size of d = 1.75 ft is required to discharge 7.5 ft³/s of stormwater.