306 Hydrostatics. 



J\C 

 or, the width of the canal being constant, as ^. We have, 



therefore, only to find when this is a minimum. It is evidently 

 equal to the diameter of the circle circumscribing the triangle 

 030"' ACB; and since the least circumscribing circle is that whose 

 centre is 1), we infer that the angle ACB of the meeting of the 

 gates should be a right angle. 



423. Water is sometimes conveyed in pipes, which, accord- 

 ing to what is above said, must sustain a pressure in proportion 

 to the height of the source. There is moreover a force exerted 



. . upon the interior of the pipe depending upon its diameter. 

 ADE being a transverse section of the pipe, let A be a par- 

 ticle of the fluid pressed by two contiguous particles B, C, and 

 kept in equilibrium by the resistance or tenacity of the sub- 



48. stance of the pipe. These three forces will be represented by 

 the three sides of a triangle formed upon their directions, or by 

 the three sides of the similar triangle OJBC, formed by lines 

 drawn perpendicularly to the directions of the forces. Now if 

 we suppose BC to become indefinitely small, or that the forces 

 exerted by B, C, are directly opposed to each other, each will 

 be represented by the radius of the section. Thus, the height of 

 the source being the same, and the substance of the pipe the 

 same, its thickness ought to be in proportion to the radius or 

 diameter of the bore. 



We may apply the same conclusion to cylindrical vessels 

 generally destined to hold fluids. Large casks are required to 

 be made stronger than small ones, in the compound ratio of their 

 diameter and height. The same precaution is to be observed, 

 moreover, with regard to steam pipes and steam boilers of diffe- 

 rent dimensions, for the above reasoning will hold true equally in 

 the case of elastic fluids, as in that of liquids. 



Solids immersed in Fluids. 



424. Since the efforts which a fluid makes in a horizontal 

 direction mutually destroy each other, in order to preserve a 



