THE JET PUMP 695 



v ? a i r i" _ Pi a i + ft a ~ P* a ^ 



or ai hi l a s h s a d h d = { a d v d * a s v* ai v^} (1) 



Again, for continuity of flow, we have : 



ai vi + a g v s = a d v d } fe> . 



or Qi + Q s = Q d ) 



From these equations, when the dimensions of the pump and the 

 heads are given, any two unknown velocities, and hence quantities, may 

 be determined. For example, if Q is given, Q s and Q d may be determined. 

 If, in addition, we assume that the pressure across the mixing chamber 

 immediately in front of the nozzle is uniform, and equal to PJ (an assump- 

 tion which is only true so long as both streams are parallel), we have 



or v? = v? - 2 g (J h + h,). (3) 



Introducing this value of v s in (1) we get : 



i hi a s h s a d h d = -^- {a d v d * (ai + a s ) vf] + a s (hi + h a ) 



or (ai a s ) In 2 a s h s a d h d = %- {^d vl (ai + a s ) VI 2 }. (4) 

 While, by substitution in (2) : 



ai vi + a s V vi* 2 g (hi + h s ) = a d v d . (5) 



From equations (3), (4) and (5), if the areas of the passages and the 

 various heads are given, the velocities vi, v s and v d , and thus the quantities 

 Qi, Qs + Qd> m ay be determined. 



EXAMPLE. 

 Thomson's Jet Pump. 



hi = 40 feet. i = -2 square feet. 



h s = 15 feet. a s = '4 square feet. 



h d = 10 feet. a d = - 6 square feet. 



Negative sign because I -rp + ^ ) is negative if h s is positi 



