FLU 



A. Figure of the secants. 



Area = r* X h. 1. S r 6 + tan ' B . 

 r 



When Q is a quadrant, area is infinite. 



Cor. The solid, generated by the revolution of the figure of the secants 

 about its base, is equal to a cylinder, the base of which is the circle, and 

 the altitude taa. 6. 



FLEXU RE point of contrary in curves. See Inflexion. 

 FLO ATING bodies. See Specific Gravity, and Equilibrium. 

 FLUENTS. See Differentials. 

 FLUIDS, pressure of.f Vince, Bland. 1 



1. The pressure of a fluid against any surface, in a direction perpen- 

 dicular to it, is as the area of the surface, multiplied into the depth of 

 its centre of gravity below the surface of the fluid, multiplied into the 

 specific gravity of the fluid ; and is .*. equal to the weight of a cylinder 

 of the same fluid, the area of whose bottom the given surface, and 

 altitude the depth of the centre of gravity. 



Hence the pressure is entirely independent of the weight of the fluid. 



.E.r. Compare the pressure on the area of a parabola with that on its 

 circumscribing rectangle, both being immersed perpendicularly to the 

 vertex. 



The areas are as 2 : 3, and the depths of their centres of gravity as 



3 1 



-jr \ -g- ; .*. the pressures are as 4 I 5. 



2. Hence if a vessel be filled Avith a fluid, the pressure on any part : the 

 Avhole weight of the fluid : : the area of that part X the depth of its cen- 

 tre of gravity ' the solid content of the fluid. 



Ex. 1. In a cone, pressure on "base 3 weight of fluid. 



2. In a cube, pressure on any side = weight of fluid. 



3. In a sphere, pressure on surface 3 weight. 



4. In a paraboloid, pressure on base 2 weight 



5. In a cylinder, pressure on bottom : pressure on th side '. : di- 



amater of base : 2 altitude. 



3. If a solid of revolution be filled with fluid, to find the pressure per- 

 pendicular to the surface. 



Let the height of the solid = *, x and y the coordinates, then the pres- 

 sure on the curve surface 



= 2 * ft, y d 2. (h *} + C. 

 ^^^ i 



