OF FLUID PRESSURE UPON THE ANNULI OF A CYLINDER. 101 



The pressure perpendicular to the base of the vessel, is 

 equal to the whole weight of the fluid which it contains. 



This is manifest, for the whole pressure of the fluid is sustained by 

 the base and the sides together, and the sides being in the direction 

 of gravity, sustain no part of the pressure which is exerted perpendi- 

 cularly downwards ; consequently, the whole weight of the fluid is 

 sustained by the base. 



3. WHEN THE PRESSURE UPON THE ANNULI OF A CYLINDER IS TO BE 



DETERMINED. 



PROBLEM XIX. 



111. If a cylindrical vessel whose bottom is parallel, and 

 sides perpendicular to the horizon, be filled with an incom- 

 pressible and non-elastic fluid: 



It is required to divide the concave surface, into any 

 number n of horizontal annuli, in such a manner, that the 

 pressure on each annulus shall be equal to the pressure on 

 the bottom of the vessel. 



Let ABCD be a vertical section, passing along the axis of the 

 cylinder, or vessel containing the fluid, whose surface 

 is AB ; draw the diagonals AC and BD intersecting 

 one another in the point p ; then is p the centre of 

 gravity of the cylindrical surface. 



Through p the point of intersection, draw the ver- 

 tical line mn parallel to AD or BC, and let a, b and c 

 be the points, which with the extremities A and D of 

 the side AD, terminate the several annuli : then, through the points 

 a, b and c, and parallel to AB or DC, draw the straight lines af, 

 be and cd, cutting BC the opposite side of the section in the points 

 f t e and d. 



Draw the zigzag diagonals Af, fb, bd and dv, intersecting the 

 vertical line mn in the points k, i, h and g ; then are the points thus 

 determined, respectively the centres of gravity of the several annuli, 

 into which the concave surface of the vessel is supposed to be divided ; 

 and n k, ni, nh and ng, are the respective depths below the surface 

 of the fluid, WP being the depth of the centre of gravity of the whole 

 upright surface of the cylindrical vessel, and nm the vertical depth 

 of the bottom. 



