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FLUID MECHANICS - CASE STUDY SOLUTION

     


Problem Diagram I

 

 

The magnitude of the resultant force is given by
      FR = ρghcA

The vertical distance to the centroid of the dam surface is given by
     hc = 700 / 2 = 350 ft

The total length L of the dam surface is calculated to be
     L = (6002 + 7002)0.5 = 922 ft

     

Problem Diagram II
 

The magnitude of the resultant force is thus given by

     FR = (1.94)(32.2)(350)(922) = 20.2 (106) lb

The coordinates for the center of pressure are given by
     

From the appendix, for a rectangle,

     Ix' = (922)3(1) / 12
     Ixy' = 0

Hence, it is found that

     xcp = xc

which is at the centerline of the dam surface. The y coordinate for the center of pressure is  

     


Pressure Prism

 

     ycp = (922)3(1) / (12)(461)(922) + 461 = 614.7 ft

The pressure prism approach can be used to verify the results obtained. Based on the pressure prism shown in the figure, the magnitude of the resultant force is represented by the total volume of the pressure prism.

     FR = Volume = 1/2 (43,730)(1)(922) = 20.2 (106) lb

This resultant force passes through the centroid of the pressure prism, which is located at a distance of 922/3 = 307.3 ft from its base and lies in the vertical symmetry axis.

     
   
 
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