CHAPTER II. 



OF THE PRESSURE OF NON-ELASTIC FLUIDS UPON PHYSICAL 

 LINES, RECTANGULAR PARALLELOGRAMS CONSIDERED AS INDE- 

 PENDENT PLANES IMMERSED IN THE FLUIDS, AND UPON THE 

 SIDES AND BOTTOMS OF CUBICAL VESSELS, WITH THE LIMIT TO 

 THE REQUISITE THICKNESS OF FLOODGATES. 



1. OF THE PRESSURE OF FLUIDS ON PHYSICAL LINES. 



THE principle established in the general proposition enables us now 

 to proceed with the resolution of a numerous class of curious and 

 important problems, which will be found of the greatest practical 

 utility, in all cases in which the pressure of watery fluids is concerned. 

 These problems we shall accompany by examples, which will unfold 

 their geometrical and analytical character, and leave no truth in the 

 phenomena of this branch of hydrodynamics unrevealed. 



PROBLEM I. 



22. A physical line,* of a given length, is obliquely immersed 

 in an incompressible fluid in a state of equilibrium, in such a 

 manner that its upper extremity is just in contact with the 

 surface ; 



It is required to determine what pressure it sustains, the 

 angle of obliquity being a given quantity. 



Let ABC, represent a vertical or upright section of a lake or 

 pool of stagnant water, confined by the walls or embankments of 

 which E E is a vertical section, and let A B be 

 the | surface of the water, supposed by the 

 problem to be in a state of equilibrium. 



In A B take any point a, and at the point 

 a thus assumed, immerse the line a b of the 

 given length, and tending downwards at the 

 given inclination or angle b a A. 



* A physical line is that which belongs to, or exists in nature, and is so called to 

 distinguish it from a mathematical line, which exists only in the imagination. 



