420 



CHAPTER XX 



These experiments show very clearly that when once a certain limit 

 has been reached prolonged spinning does not further decrease the water 

 content. If the limit to which the water can be removed is reached when 

 the centrifugal force balances the force due to surface tension between the 

 crystal and the liquid, it follows that prolonged duration of rotation will not 

 further decrease the water content after these forces are once balanced. 



The drainage of molasses from a massecuite in a centrifugal may be 

 considered as a special case of the flow of a liquid through a system of capillary 

 tubes, which are formed by the interstices between the crystals. The equation 



for this flow is given by Poiseuille's law,^ in which F = C X -^ — ^ where d 



is the diameter of a tube of length I, p is the pressure, w is the viscosity, 

 F is the rate of flow and C is a constant. The pressure acting on the molasses 

 varies as the square of the number of revolutions and hence also does the 

 rate of flow. The time required to expel the molasses should then decrease 

 with the speed and should be accompanied by an increase in the capacity 

 of the machine. 



Fig. 265 



Fig. 266 



The deciding factors governing the economical speed are prime cost and 

 strength of materials taken together. It does not appear probable that 

 in the sugar industry there will be any departure from the present standard 

 practice as regards speeds, which are those given in the table above and are 

 based on equal centrifugal force and 1,200 r.p.m, in a 30-inch machine. 



Size of Grain as affecting Centrifugal Capacity. — Consider a square of 

 side one unit in length in which there are arranged n^ circles each of diameter 



as in Fig. 265. 



The area occupied by the circles is w^ x — x -^ 



A n^ 



constant, and the sum of the interstitial spaces between the circles is i — - 



4 

 which is also constant. Hence whatever be the diameter of the circles the sum 

 of the areas of the interstitial spaces is the same. In the case of a massecuite 

 contained in a centrifugal basket the interstitial spaces between the crystals 

 rhay be considered as forming a system of capillary tubes through which 

 the molasses flows under the influence of the pressure due to the centrifugal 

 force. If d be the diameter of a circle in Fig. 265 the " diameter " of an 



