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FLUID MECHANICS - CASE STUDY SOLUTION


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) = 53.1o

The wetted perimeter P is given by

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

The cross sectional area A is determined as follows:

     A = πd2/4 - AI + AII

where
     AI = 2(53.1o/360o)(πd2/4) = 0.221d2
      
AII = 2(0.3d)(0.3d tan 53.1o)/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.

     
   
 
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