

PRESSURE AT ANT POINT OF A ROTATING LIQUID. 87 



EXAM PLES. 



1. If the vessel (Fig. 15) contain a liquid, and make 30 

 revolutions per minute, find the value of NM. 



Here w = 2rr x 30-5-60 = TT, and g = 32 ; therefore we 

 have, from (2), 



qo 



NM = -, = 3.242 ft. = 38.9 in. 



7T 2 



2. If the vessel make one turn in a second, find the value 

 ofNM. Ans. 9.72 in. 



3. If the vessel make 95 turns per minute, find the value 

 ofNM. Ans. 3.88 in. 



22. The Pressure at any Point of a Rotating 

 Liquid. Let ABCD be a vertical section through the axis 

 of a vessel containing a rotating 

 liquid ; let Q be any point (x, y] in 

 the liquid referred to the rectangu- 

 lar axes OX, OY, and describe a 

 small vertical prism having Q in its 

 base, which is to be taken hori- 

 zontal. 



The prism PQ of liquid rotates 

 uniformly under the action of the 

 pressure around it, but its weight is 

 entirely supported by the vertical pressure on its base. 

 Hence, if p be the pressure, and p the density, we have 



(1) 



Fig. US 



P = 

 But [Art. 21, (2)], 



PQ = OM - ON = 





- ON, 



which in (1) gives, 



p = 



(3) 



