160 



EFFLUX FROM A ROTATING VESSEL. 



COR. 3. If in (1), P = Q, then / = 0, and the vessel 

 is at rest. If P < Q, then Q will descend and P ascend, 

 / is negative and (3) becomes 



v = V2 (g -f) h, 



and the vessel descends with an accelerated motion, the 

 velocity being diminished. 



COR. 4. If P = 0, then, from (2),' g +f= 0, and 

 therefore, from (3), v = 0, and there is no pressure on the 

 bottom of the vessel, and no liquid will flow out; which is 

 also evident from this, that every particle in the vessel will 

 descend by its own gravity, with the same velocity. 



89. Efflux from a Rotating Vessel. If a vessel 

 ABCD, containing a liquid, is made to rotate about its ver- 

 tical axis XX', the surface of the liquid 

 will take the form of a paraboloid of revo- 

 lution (Art. 21), and at the centre H of the 

 bottom the depth of liquid KH is less than 

 it is near the edge, and the liquid will flow 

 more slowly through an orifice at the centre 

 than through any other orifice of the same 

 size in the bottom. 



Let h denote the height KH ; then the 

 velocity of efflux through an orifice at H = 

 Vfyh> Let y denote the distance HO = 

 MP of an orifice from the axis XX', and w the angular 

 velocity ; then, since the subtangent MT is bisected at K, 

 we have, for the height of the liquid at P above the centre K, 



KM = 



tan MPT 



MP 



MN 



[from (2) of Art. 21]. 



