ROTATING LIQUID. 



35 



14 ft, and its base is 6 feet. Show that the wall will be 

 overthrown by the pressure of water against it, when it rises 

 to the top of the wall. 



21. Rotating Liquid. It has been shown (Art. 11) 

 that, if a liquid at rest be subject to the force of gravity 

 only, its free surface must be horizontal, i. e., everywhere 

 perpendicular to the direction of gravity. In the same way 

 it may be shown that, if a liquid be subject to any forces 

 whatever, its surface, if free, must at every point be per- 

 pendicular to the resultant of the forces which act upon 

 that point. For, if the resultant had any other direction, 

 it could be resolved into two components, one in the direc- 

 tion of the normal and the other in the direction of the 

 tangent ; the first of these would be opposed by the reac- 

 tion of the surface ; the second, being unopposed, would 

 cause the particle to move, which is contrary to the hypoth- 

 esis that the surface is at rest: hence the surface is at every 

 point perpendicular to the resultant of the forces which act 

 upon that point. 



If a quantity of liquid in a vessel be made to rotate 

 uniformly about a vertical axis, the surface of the 

 liquid will take the form of a paraboloid of revolu- 

 tion. 



Let ABCD represent a vertical section 

 made by a plane passing through ZZ', the 

 axis of rotation of the vessel containing 

 the liquid, and let the curved line AVD, 

 represent the section of the surface of 

 liquid made by this plane, and let P be 

 any point taken on this section. 



Now every particle of the liquid moves 

 uniformly in a horizontal circle whose 

 centre is in the axis ZZ', and there- 

 fore is urged horizontally by a centrifugal force directed 



