200 OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 



the base, supposing the water to be on a level with the top of the 

 wall, the specific gravity of the materials of which it is built being If, 

 that of water being unity ? 



Let these numbers be substituted for the respective symbols in the 

 above equation, and we get 



b* 26 61.619, 

 complete the square, and it becomes 



&* 26+ 162.619, 

 from which, by evolution and transposition, we get 



b 8.9 13 feet nearly. 



Here then, the transverse section of the dyke is 8.913 feet across at 

 the bottom, and consequently it is 8.913 4 4.9 13 feet broad at 

 the top ; hence the delineation is very easily effected. 



215. If the slope c should vanish; that is, if 

 the side of the dyke on which the fluid presses A.JB 



be vertical, as represented by A BCD in the an- 

 nexed diagram ; then S vanishes also, and the 

 equation marked (149) becomes 



(155). 



where it is manifest there is no vertical pressure 

 on the dyke, the whole effect of the fluid being exerted in the hori- 

 zontal direction, tending to turn the wall about the remote extremity 

 of its base. 



When the perpendicular altitude of the wall or dyke, and the depth 

 of the water are equal ; then dizzo, and admitting that the value of 

 5, or the specific gravity of water is represented by unity, we obtain 



and this, by transposition and division, becomes 



*-=^' 



and lastly, by extracting the square root, we get 



' y 



(156). 



Let the slope of the dyke be two feet, its perpendicular altitude, or 

 the depth of the fluid 20 feet, and the specific gravity of the material 

 If, as in the preceding example; then, by substitution, we obtain 



6= i / 400 +" = 8.804 feet. 

 V 3X1.75 



