Problem Diagram I

The magnitude of the resultant force is given by
      F_R = ρgh_cA

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

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

The magnitude of the resultant force is thus given by

     F_R = (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,

     I_x' = (922)³(1) / 12
     I_xy' = 0

Hence, it is found that

     x_cp = x_c

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

Pressure Prism

     y_cp = (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.

     F_R = 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.