THEORY OF CREAM SEPARATION. 257 



" *' 30 V 



2(d, -djl b^ 



which expreaaes the time taken for a globule to pass from any point in the 

 separator to any other point, provided the serum is at rest and the globule 

 travels radially. 



This is not the case in modern separators where the milk runs in con- 

 tinuously, and terms expressing the rate of flow of milk, and the shape 

 of the separator, must be introduced. The resulting equations are so 

 complex that it would serve no useful purpose to deduce a general equation. 



Whatever the form of equation suited to any particular separator, the 

 time taken by a globule to pass through a given space will always be pro- 

 portional to the square root of the cube of the radius, and as the number 

 of gallons per hour passed through the separator will be inversely propor- 

 tional to the time, it follows that for each size of fat gobule there will be 

 a limit where its velocity against the stream of milk wiU be equal to the 

 velocity of the stream itself, and all globules smaller than this wiU pass 

 out with the separated milk. If we assume that the total weight of fat 

 in globules of any size is equal to the total weight of fat in globules of any 

 other size, it follows that the amount of fat in the separated milk is pro- 

 portional to the cube root of the square of the number of gallons per hour 

 The coefficient of viscosity, and also the value of the factor (</, — di), ^ary 

 with the temperature, and consequently the viscosity of the fat globules 

 and the amount of fat in the separated milk. 



The relative proportions of the cream and skim milk will also effect the 

 percentage of fat in the separated milk, as not only is the rate at which 

 milk travels towards the separated milk outlet effected, but any resistance 

 to the exit of cream causes the fat globules to touch each other, and interferes 

 with their free motion. 



The author has, upon tlieso considerations, worked out a formula to 

 give the percentage of fat in the separated milk — 



f = axb ' X C' X ™ , 



(■- 



where / = percentage of fat in separated milk, 

 F = ,, ,, cream, 



t = temperature in degrees Centigrade, 

 m = number uf gallons per hour, 

 V = „ revolutions per minute. 



a, b, and c are constants for each separator. 

 b usually varies from 1-03.5 to 1-05. 

 c „ „ from 1-00 to 1-05. 



c is appreciable, chieiiy with separators in which the adjustment of the 

 thickness of the cream is made at the cream outlet — e.g., in the Alpha 

 separator, in which c has the value lui to 105. 



The following results were obtained with a separator, for 

 which the following formula was applicable : — 



I = 8,155 X 1040 ' X 10471 X 



.a 



17 



