ON THE FLOW OF WATER THROUGH ORIFICES. 



257 



that reasoning being now applied to the two flows commencing at the initial 

 interfaces BCD and B' C D', and continued to the terminal interfaces F V 

 and F' F', it results that if the jet in No. 1 be allowed to flow freely to and 

 far past the interface F F, the jet in No. 2 terminating at F' F' can be 

 left to flow unguided, with stream-lines similar to those in No. 1 , and with 

 the same relations of pressures and velocities at its various places to the 

 pressures and velocities in No. 1 as have been already proved for the flow 

 terminating at E' E', provided that homologous pressures »i^ times those at 

 F F be anyhow maintained at F' F'. Thus, then, we see that if adjusted 

 or requisite pressure systems, such as have been already fully exjilained, be 

 maintained at F F and F' F', the two streams, one extending backward • 

 from FF to E E, and the other from F' F' to E'E', will transfer backward 

 just such pressures to successive places in retrograde order in their courses 

 as that they will of themselves apply, at the interfaces E E and E' E', ex- 

 actly the already specified requisite pressure sj'stems. Thus we can depart 



Fig. 9. 



No. 1. 



No. 2. 



as far as we please from the orifices forward along the two streams to the 

 places where, for purposes of reasoning, certain definite pressures are to be 

 supposed to be applied in two homologous cross interfaces. Now it may be 

 taken as evident that, by going far enough away from the orifice to the 

 terminal cross interface, we can make, for any disturbances or departures 

 from the specified pressure relations, the effects propagated backwards to 

 the water in and near the orifices as small as we please ; or that, even if 

 we were to apply not exactly the strictly requisite pressure systems at those 

 terminal places, still the effects of this departure from perfect exactitude 

 would fade away rapidly in either stream as we transfer the place under 

 consideration backwards against the current towards the orifice. In corro- 

 boration of this, observation on the flow of water spouting from an orifice 

 may be appealed to as setting this matter beyond doubt, through its showing 

 that any changes of pressure introduced in a jet of water at any place far 

 1876. s 



