80 



DAMS AND HEADWORKS 



as follows: Draw af equal to cd and ec equal to ab. Divide ab 

 and cd in two equal parts and connect the dividing points. Con- 

 nect e and /, and the point where these two lines intersect is the 

 center of gravity. It may also be calculated from the following 

 formula: 



ff* 



_H H/cd-ab\ 

 "2" 6V 



cd+ab/' 



The cross-section A of the dam can be figured from the 

 formula: 



and by multiplying this by the weight of masonry, 150 Ibs. per 

 cu. ft., the weight of the dam per foot length is obtained. 



The factor of safety 

 against overturning S of 

 the structure is: 



Water Level 



8 = 



W Xdi 

 PXdk' 



FIG. 34. Cross-section of Gravity Dam 

 (Water overflowing). 



It is seen that the greater 

 the inclines of the sur- 

 faces the more stable 

 will the structure be. 



In the above it was 

 assumed that the water 

 was level with the crest 

 of the dam. Suppose 

 now that the water is 

 flowing over, as in Fig. 



34. In this case the pressure P is equal to 



62.4^^W-/OXsec = 62. 

 * / 



sec pounds. 



This pressure is, however, not applied at a point f // from the top, 

 as in the previous case, but at a point x from the top, this distance 

 being equal to 



Z = 



