THE EXTRACTION OF THE JUICE BY MILLS 



191 



In the table above is also given the volume of the residue, R, and values 

 of RP-^. 



The curves given in Figs. 78 and 79 are the converse of each other ; in 

 both, the curve begins to bend from the horizontal or the vertical at about 

 500 lbs. per sq. in. pressure, and assumes the vertical or horizontal at about 

 2,000 lbs. per sq. in. pressure. After this press\ire has been reached, great 

 increases in pressure are accompanied by relatively very small increases 

 in the volmne of juice expressed and by very small decreases in the volume 

 of the bagasse or cane fibre. 



The writer does not wish to be understood as expressing the opinion 

 that these relations are absolute ; they are rather of the nature of approxi- 

 mations, and probably the real relation is of the form VP-^^''' = constant, the 

 exponent increasing as P increases. 



Work done and Power absorbed in compressing. Bagasse. — Allowing that 

 the relation, H°P = constant, represents the behaviour of bagasse on pressure, 

 the work done in passing from a volume Fj to a volume Fg is 



KH-^ dv 



Consider the case of a column of bagasse on a base oi i sq. in. and 0-6 

 inch high, which is to be compressed to 0-25 inch high. Then the work done 

 in compressing is 



KH-^ = ~ (" 0-6-*- 0-25-^) 



In the experiment quoted previousl}' the value of H^ P is about 9-5, 



so that the value of the integral in this particular instance is 590-1 inch-lbs. 



or 49-2 foot-lbs. A 78-in. mill describes 23,400 sq. in. in one minute, 



and grinds 100,000 lbs. of cane with 12 per cent, fibre in one hour. The 



work done in one minute is then 49-2 X 23,400 = 1,151,280 ft.-lbs., which 



1,151,280 -.-. „ 



requires — ^^— = 35 H.P. 



^ 33,000 



This result, of course, refers to the actual 

 work done in one compression according to 

 the observed data, and does not include 

 the work represented by friction, trans- 

 mission of power, etc. 



The work done in compressing fibre 

 under the equation, H^P = K, is independent 

 of the way the pressure is applied. In Fig. 80 

 let 11 = the specific normal pressure on a 

 small particle of bagasse, and let t be the 

 specific tangential pressure causing unifoiTn 



motion of the particle. Then the condition of equilibrium of the particle 

 of bagasse is 



t ds cos a = \ nd s sin a 

 If a is small, cos a = i and 



ra re 



t ds = \ n ds sin a. 



J A J A 



