4i8 CHAPTER XX 



n will be 16 and r for a particle on the shell of the basket will be 1-75, so 

 that the value of the above expression is 553, i.e., the force at the periphery 

 tending to drive the molasses through the screen is 553 times that due to 

 gravity. 



Power used in Centrifugals. The work done on a particle in reaching a 



W v 2 

 speed v is , where W is the weight of the particle. In the case of the 



machine considered above, the basket weighing 270 Ibs. attains a speed of 

 183 ft. per sec. in, say, one minute. The load of 600 Ibs. reaches in the same 

 time a speed of 157 feet, and the rest of the machine, spindle, top and bottom 

 of basket, pulley, etc., may be taken as weighing 300 Ibs. and acting at a 

 radius of one foot to reach a speed of 105 feet. 



Wv 2 

 The value of for these three items is 505,000 foot-pounds, and the 



average power developed, neglecting windage and friction, will be 505,000 4- 

 33,000, or 15 3 H.P. Since at the commencement of the operation the power 

 is zero, the maximum power developed, assuming uniform acceleration, 

 will be twice the average or 30 6. This quantity will be reduced if molasses 

 are thrown off during acceleration, as is actually the case. When speed is 

 reached only the power to overcome friction and windage is required, and 

 eventually during the period of slowing down and discharge no power is 

 consumed. 



Provided the prime motor has sufficient power to keep the machine 

 running at full speed, this speed would eventually be attained, though 

 without an excess of power the period of acceleration may be so prolonged 

 as to cut down the capacity of the battery materially. This point is of 

 importance as regards the choice of drive, and is discussed elsewhere. 



Some actual results given the writer by Mr. W. G. M. Phillips follow : 



A 40-in. x 24-in. machine with motor attached to spindle consumed 

 45 H.P. when reaching a speed of 1,060 r.p.m. in 70 seconds, falling to 21-5 

 H.P. when the time to full speed fell to 150 seconds. 



With eight 4O-in. X 24-in. machines and mixer, belt-driven off a motor, 

 the electrical input averaged over a long period and obtained from a recording 

 instrument was 60 kw., corresponding at 90 per cent, efficiency to 72-5 H.P. 

 delivered to the machines, or to 9 06 H .P. per machine. The sugar produced 

 per hour was 26,650 Ibs. Evidently in machines working up low sugars 

 where the acceleration period is only about 10 per cent, of the total time of 

 operation, the power required is much less. 



With smaller machines the power required is roughly proportional to 

 the decreased output, increasing, however, more rapidly than the output 

 decreases, since the dead load carried is greater in proportion with the smaller 

 machines. Further, in installations of fewer machines the power per unit 

 must be increased, since the demand for power will not be so evenly averaged. 



Centrifugal Speeds. In discussing centrifugal speeds the distinction 

 between equal speed and equal centrifugal force must be recognised. Evi- 

 dently if D be the diameter of the basket and if N be the revolutions per 

 minute for equal peripheral speed, DN = constant. The equation for equal 

 centrifugal force, however, is DN 2 = constant, and accordingly as the dia- 



