OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 199 



if all the terms of this equation be divided by 225, the co-efficient of 

 b*, we shall get 



b* 6 = 61.856, 

 and this, by completing the square, becomes 



therefore, by extracting the square root and transposing, we have 

 b rz 8 . 1 4 feet nearly. 



COROL. It therefore appears, that under the same circumstances, 

 the computed breadth of the foundation differs very little, when the 

 vertical pressure of the fluid is considered, from what it is when the 

 pressure is omitted ; and what is very remarkable, the difference, 

 whatever it may amount to, leans to the side of safety and conve- 

 nience in the case of the omission ; it will therefore be sufficient in 

 all cases of practice, to employ equation (150), but under certain 

 circumstances of the data, it will admit of particular modifications. 



213. When the slopes c and e are equal ; that is, when the vertical 

 transverse section of the dyke or embankment, 



is in the form of the frustum of an isosceles 

 triangle, as represented by ABC D in the annexed 

 diagram ; then, the general equation (149), be- 

 comes transformed into 



sd*=idSs(3b S) + 36D/(6 c). (151). 



If the perpendicular height of the dyke, and 



the depth of the fluid, are equal to one another ; that is, if the water 

 is on a level with the top of the wall ; then, rfzz D and 3 = c, and the 

 above equation becomes 



sd* = cs(3b c) + 3bs'(b c). (152). 



Again, if we neglect the effect of vertical pressure, and express the 

 specific gravity of water by unity, we get 



3s'(tf cb) = d\ (153). 



And finally, if both sides of the equation be divided by the quantity 

 3/, we shall obtain 



b *- cb = 37- (154). 



The method of applying this equation is manifest, for we have only 

 to substitute the given numerical values of c, d and /, and the value 

 of b will become known by reducing the equation. 



214. EXAMPLE 2. The dyke or embankment which supports the 

 water in a reservoir, is 20 feet in perpendicular height, and it slopes 

 equally on both sides to the distance of 2 feet ; what is the breadth of 



