92 



Dr. W. J. M. Ilankine on the 



[Recess, 



second law of motion, the difference between those impulses is equal to the 

 change of momentum produced ; that is to say, 



A(P,^J €^mi\ >-V) } , .... (2) 

 or dividing both sides by A, 



p ^ L ^-r s {£^- v >} • • • • < 2A > 



And this is the general dynamical equation of the combination of any 

 number of streams of any fluids. 



If the preceding equation, as applied to a combination of two streams 

 only, be compared with the equation not numbered, which immediately 

 precedes equation 60 in Zeuner's treatise, it will be seen that they are 

 virtually identical, although different in form, and demonstrated by different 

 methods. 



5. Loss of Energy at Junction. — If a given mass of any fluid at the 

 bulkiness s and pressure p is contained in a reservoir, from which it is 

 capable of being expelled by the inward motion of a piston loaded with an 

 external force equivalent to the pressure, it is known that the potential 

 energy of the mass of fluid and of the piston relatively to a point at the 

 level of the centre of mass of the fluid is expressed by multiplying the 



mass by ^ SC ^P> the relation between 5 and p being that which is called 



adiabatic ; that is to say, such that no heat is received or given out by the 

 fluid. Hence the loss of energy in the junction- chamber in each unit of 

 time is given by the following expression : — 



'{«'*)}-«(? + j>> 



of which the first, or positive term, denotes the aggregate energy, actual 

 and potential, of the component streams as they enter the junction- cham- 

 ber ; and the second, or negative term, expresses the total energy, actual 

 and potential, of the resultant stream as it leaves that chamber. That lost 

 energy takes the form partly of visible eddies and partly of invisible 

 molecular motions — that is, of heat. 



The integral expressing the aggregate potential energy of the component 

 streams may be put in the following form : — 



(3A) 



If no change of total bulkiness arises from the mixture of the component 

 streams, the volume occupied by a given mass of the mixture is simply the 

 sum of the volumes of its ingredients ; so that we have 



; (3B) 



S *o ' 



