108 OF FLUID PRESSURE UPON THE INTERIOR OF CONICAL VESSELS. 



Let this value of d be substituted instead of it, in the equation 

 marked (74), and we shall have for the pressure on the curved surface 

 of the vessel 



p .5236 D s (2/3 4- 3) V^-4- J03 3)* ; (75). 



consequently, by comparing the equations (72) and (74), we get 

 Pip:: .7854/3*DS : .5236 D s(2/3 + 3) J D 2 



and this, by suppressing the common factors, becomes 



P : p : : 3/3* : 2 (2/3 + 3) V* + i (P - *)- (76). 



If J, the upper diameter of the frustum vanishes, the figure becomes 

 a complete cone, and consequently, the pressure upon the base, is to 

 that upon the curve surface, as three times the diameter of the cone, 

 is to four times its slant height ; that is 



P:p:: 3/3: 4^+1^. (77). 



According to the principles of solid geometry, the capacity of the 

 conic frustum, or the quantity of fluid which the vessel contains, is 



where c denotes the solid content of the vessel. 

 But the weight of any quantity or mass of fluid, varies directly as 

 the magnitude and specific gravity conjointly; consequently, the 

 weight of fluid in the vessel, is expressed by 



w .2618 D s (/3 s + /3 J -f a 2 ). (78). 



Hence, if the equations marked (72) and (78), be compared with 

 each other, we shall obtain 



p^i-.s/^os'-h/sa+a 2 ), (79). 



and when 3 vanishes, the vessel becomes a complete cone, and conse- 

 quently, we get 



P : w : : 3 : 1, (80). 



It therefore appears, that the pressure against the bottom of a 

 conical vessel, when filled with an incompressible and non-elastic 

 fluid, (the bottom being downwards) : 



Is equivalent to three times the weight of the fluid which it 

 contains. 



The solidity of the cylinder circumscribing the conic frustum, of 

 which abci> is a vertical section, is 



c' =r.7854 f? D, 

 where c' denotes the capacity of the cylinder circumscribing the vessel; 



