Air-Water Jet (Mist-Jet) for Ship Propulsion 



(l+r)2 ^v RT dP T^^D^ dx ,.,:.•;. 



-^ — V — = (1 + a) 



(1 + rcx) ge M ' P p^ Ag 



as the differential equation relating momentum velocity to pressure and distance 

 in a two -phase expansion nozzle. 



Looking next at the particle momentum equation, and rearranging gives 



dx . 



But 



and 



Vn 4 D Pi 0-2 





^^g ^ dV_ ra da T ' v , 



V, ' V ' 1 + •--" ' '■'■ ^ ■ ■ 



so that the particle equation can be rewritten as 



dV 1 da _ 3 ^D ^g (1-^)^ ^^^ 



V 1 + ra ^ 4 D Pi a^ 



There are now two equations for momentum mean velocity for the two -phase 

 nozzle which give v in terms of pressure, distance, and slip ratio. For the 

 purposes of this analysis it will be assumed that the slip ratio is constant along 

 the nozzle length. This is not meant to be a requirement for such nozzles, but it 

 does permit straightforward integration of the momentum equations. 



Taking first the total momentum equation, it may be reasonably assumed 

 that a << 1 for a Mist-Jet type nozzle, thus 



_ ~ 2 

 P V^^ 



A = A„ , and T, ., =^ f 



SO that, upon integration, 



2(1+ ra) f r r + 1") ~ T 



V 2 _ V.2 = - -^ (P )2 In (P /P. ) - ^ ^ V 2 -±- 



(1+ r)2 ^ ^^ ^ e W 2 ^ D^ 



or 



f (r+ 1) l\ V (1+ra) /C^\' 

 1 + -^ — H^ - 1 = -2 [-J-] in (P /P: ) . 



1065 



