99 



2. WHEN THE VESSEL IS IN THE FORM OF A CYLINDER. 



PROBLEM XVIII. 



109. If a cylindrical vessel be completely filled with an 

 incompressible and non-elastic fluid, and so placed, that its 

 bottom may be parallel to the horizon: 



It is required to compare the pressure against its bottom, 

 with that against its upright surface, and also with the 

 weight of the fluid which it contains. 



Let ABCD be a vertical section of a cylindrical vessel, filled with 

 an incompressible and non-elastic fluid, whose 

 surface AB is horizontal, and let it be required 

 to compare the pressure exerted by the fluid on 

 the bottom DC, with that upon the whole upright 

 surface. 



Draw the diagonals AC and BD intersecting 

 one another in the point p, and through the point 

 p, draw the vertical line mn, meeting DC the 

 bottom of the vessel in the point m, and A B the surface of the fluid in 

 n; then is m the position of the centre of gravity of the bottom, and 

 nm its perpendicular depth below the surface AB. 



Bisect AD in E, and through E draw EP parallel to A B or DC, and 

 meeting the vertical line mn in p ; then is p the position of the centre 

 of gravity of the upright surface, and n p its perpendicular depth below 

 AB the surface of the fluid. 



Put D nz AB or DC, the diameter of the cylindrical vessel proposed, 

 d ~ nm, the perpendicular depth of the centre of gravity of the 



bottom DC, below AB the surface of the fluid, 

 3 ~ nv, the perpendicular depth of the centre of gravity of the 



upright surface, 



Anr the area of the base or bottom of the cylinder, 

 P the pressure upon it, 

 nz the area of the curved or upright surface, 

 p the pressure upon it, 

 w zzz the weight, 

 and s z= the specific gravity of the fluid. 



Then, by the principles of mensuration, the area of the base or 

 bottom of the cylindric vessel, is 



A=r.7854D 2 , 

 H 2 



