OF FLUID PRESSURE UPON THE ANNULI OF A CYLINDER. 105 



113. And from the above general form of the equation, the follow- 

 ing practical rule may be derived, for calculating the breadth of any 

 proposed annulus, independently of the breadths of those which pre- 

 cede it. 



RULE. From the square root of the number which expresses 

 the place of the required annulus, subtract the square root of 

 that number minus unity ; then, multiply the remainder by 

 the geometric mean between the altitude of the vessel and the 

 radius of its base, and the product will give the breadth of the 

 required annulus. 



114. EXAMPLE. A cylindrical vessel has the radius of its base, and 

 its perpendicular depth, respectively equal to 4 and 24 feet; now, 

 supposing the concave surface to be divided into 6 horizontal annuli, 

 such, that the pressure upon each shall be equal to the pressure upon 

 the base ; required the breadth of the fourth annulus ? 



By performing the operation as directed in the preceding rule, we 

 shall obtain 



x'" (^ V3)X v/4 X 24 z=2.625 feet nearly. 



The annulus which we have just determined, corresponds to the 

 fourth of the preceding class of equations, or that marked (69), and 

 the distance of its centre of gravity below the surface of the fluid, or 

 its position with respect to the bottom or top of the vessel, can easily 

 be ascertained. 



The area of the cylinder's base, is 



A 3.1416B 9 ; 



the pressure which it sustains, is 



p = 3. 1416 R 2 d= 1206.3744, 



and this is equal to the pressure on the annulus. 



Now, according to the writers on mensuration, the area of the 



annulus, or the curved surface of a cylinder, whose radius is 4 feet 



and its perpendicular altitude 2.625 feet, is expressed as follows, viz. 



6.2832 X 4 X 2.625 = 65.9736. 



If therefore, we divide the pressure on the base of the vessel, by the 

 area of the annulus, the depth of its centre of gravity will become 

 known ; thus, we have 



