EVAPORATION 329 



cell from which steam is not separated ; let F be the steam which must be 

 supplied to the first cell. Then — 



n Z + ^1 + 2/^2 +3ps + ■ ■ ■ • +np„ = E 



+ />! + ^2 + • • • • + A. 



n 

 The total consumption of steam is then — 



E 

 Without separation of steam the consiimption was -- +0, so that the 



• Pi — -P-2 — — -+- "A. 



savmg^ is -^ ~^ -^ . 



Now with an apparatus of n effects, let an independent apparatus be 

 installed, to which p^ steam is delivered, and from which />„ steam is gener- 

 ated, and used towards doing the work represented by ; then using the 



same notation as before, S =//—/>„ -^ —. and the saving is — , the 



« ° n 



same as if p^ had been separated from the first cell of a multiple of n effects. 



The pre-evaporator may also be a double or even a triple effect apparatus, 



E ffi f) 



in which case S = H — m pQ -\ ~, and may also be operated in 



connection with a multiple from which steam is separated, when the value 



of .S becomes H - m p, + g- >np^~ p^ - 2 p^ - .... np„ ^^^^^^^ ^ 



n 

 is the number of effects in series in the pre-evaporator and the other s\TTibols 

 are as before. 



From the above it follows that the maximum econoni}- is reached when 

 the steam delivered to the multiple is equal to that required for obligatorv 



E 

 single effect evaporation ; that is to say, when — = 0. In an\- case, the 



economy increases as the steam separated for obhgator}' single effect evapora- 

 tion is taken from a vessel later in series. 



The actual working Umit of economy is controlled by the following 

 factors : — 



1. The value of n cannot be indefinitely increased, since the upper limit 

 of temperature to which sugar solutions maybe exposed without destruction 

 is about 260 "^ F., and the lower limit obtainable by reduction of pressure 

 is about 120" F. 



2. As the value of n increases, the cost of apparatus in relation to capacity- 

 also increases. 



3. The utilization of steam at lower temperatures is limited, since the 

 necessities of manufacture require juices to be heated to about 212" F. 



4. No economy obtains if the consumption of steam is reduced below 

 that corresponding to the production of exhaust steam from the engines, 



