OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 191 



section, intended as a preliminary article to our Inland Navigation, 

 which will consequently form a part of Hydraulic Architecture. 



205. When an incompressible and non-elastic fluid presses against 

 a dyke, mound of earth, or any other obstacle that it endeavours to 

 displace, there are two ways in which the obstacle thus opposed may 

 yield to the effort of the fluid. 



1 . It may yield by turning upon the remote extremity of 

 its base. 



2. It may yield by sliding along the horizontal plane on 

 which it stands. 



In either case, the effort to overcome the obstacle, arises from the 

 force which the fluid exerts in a horizontal direction ; and the stability 

 of the obstacle, or the resistance which it opposes to being overcome 

 or displaced, arises from its own weight, combined with the vertical 

 pressure of the fluid upon its sloping surface. 



206. When the vertical pressure of the fluid is considered, the 

 investigation, as well as the resulting formulae, a're necessarily tedious 

 and prolix ; but when the effect of the vertical pressure is omitted, the 

 subject becomes more easy, and the computed dimensions are better 

 adapted for an effectual resistance ; but in order to render the inves- 

 tigation general, it becomes necessary to include its effects. 



Now, it is manifest from the nature of the inquiry, that when an 

 equilibrium obtains between the opposing forces, the momentum of 

 the horizontal pressure must be equal to the momentum of the vertical 

 pressure, together with the weight of the body on which the pressure 

 is exerted ; and for the purpose of showing when this condition takes 

 place, let A BCD represent a vertical section 

 of the dyke, whose resistance is opposed to 

 the pressure of the stagnant fluid, of which 

 the surface is ME and the perpendicular 

 depth EF. 



Let AB and DC be parallel to the hori- 

 zon, and consequently parallel to one another; and from the points 

 E, A and B, demit the straight lines EF, AK, and BL, respectively 

 perpendicular to DC the base of the section. 



Take EG any small portion of the sloping side AD, and through 

 the point G, draw the lines GH and 01, respectively parallel and 

 perpendicular to the horizon, constituting the similar triangles EHG, 

 EFD and GID. 



The figure being thus prepared, it only remains to establish the 

 proper symbols of reference, before proceeding with the investigation. 



