12 OF THE PRESSURE OF FLUIDS ON PHYSICAL LINES. 



is just in contact with the surface, and the other inclining downwards 

 in an angle of 67 35'; what pressure does the line sustain, supposing 

 the fluid in which it is placed to be in a state of equilibrium ? 



Here by the question, the fluid in which the line is supposed to be 

 immersed is water, of which the specific is unity; consequently, 

 according to the rule, we have 



p zz 36 X 36 X \ X sin. 67 35' ; 



but by the Trigonometrical Tables, the natural sine of 67 35' is 

 .92444 ; hence we get 



p=\296 X J X .92444 = 599.03712. 



In this case, however, the resulting pressure is only relative, the 

 absolute pressure being indeterminable, upon a line where length 

 merely is indicated and no breadth assigned ; the existence of surface 

 being indispensable for the expression of a determinate measure. 



25. If the line were immersed perpendicularly in the fluid, or so 

 as to make a right angle with its surface, the equation (3) would 

 become transformed into 



p=%sl*sin. 90; 

 but by the principles of Trigonometry, we have 



sin. 90 = 1 ; 

 hence, by substitution, we obtain 



j.= JP; (4). 



and this, in the case of water, where the specific gravity is unity, 

 becomes 



P =ii*. 



Therefore, the relative pressure for a perpendicular immersion, on 

 the line, as given in the above example, is 



p = 36*36* 1=648. 



26. If the upper extremity of the line be not in contact with the 

 surface of the fluid, but placed as in the 



annexed diagram, then the method of solu- 

 tion, and consequently the form of the re- 

 sulting equation, will be somewhat different. 



Let A B be the surface of the water or 

 fluid in which the line is immersed, and 



A B c D a vertical section, in whose plane the line a b is situated, E E 

 being the corresponding section of the walls or embankments by 

 which the fluid is contained. 



Bisect the given line ab in m, and through the point m thus deter- 

 mined, draw m n perpendicular to A B, the surface of the fluid ; and 

 through a and b the extremities of the given line, and parallel to mn, 

 draw ad and be, and produce ba to meet AB in A, or in any other 



