

JET PEOPULSION 405 



engines, and is then discharged directly astern. The escaping 

 stream, in virtue of its reaction on the vessel, does work in propulsion, 

 while the theoretical efficiency of the system may be calculated as 

 follows : 



Let A = sectional area of discharge orifices in square feet. 



u = velocity of vessel in feet per second. 



v = velocity of efflux of stream relative to boat. 



Then v u = absolute velocity of efflux of stream, i.e., its velocity 

 relative to the surrounding water. 

 The initial velocity of the \ 

 water before being drawn ; = 



into the vessel 



Its final velocity in the direc- \ =u _ v ft sec . 

 tion of motion of the vessel J 

 The weight of water dis- \ =WAv lbs> 



charged per second 

 .-. The change of momen- j 



turn of the water in the ( W A v , 



, V = - - (v u) per sec. 

 opposite direction to that of { g 



motion of the vessel ) 



W A v 



Propelling force on boat = - - (v u) Ibs. (1) 



Work done in propulsion 1 WA v u , , ., /ON 



- (v u) ft. Ibs. (2) 



per second J g 



Kinetic energy rejected per 1 WA v 2 



i . 1 1 i i r ~ V" ~~~ '"/ I". lUb. V.O) 



second in the discharge J 2 # 



/. Total energy given to I w / ^ r /- ^ 



water per second neglecting I - - J (v u} 2 -J- 2 u (v u) I ft. Ibs. 

 eddy and frictional losses j 



W A v 



: 



Theoretical efficiency of ) useful work done by jet _ 2 u (v u} 

 jet J energy given to jet v* u 2 



= ~~. (5) 



v -f- u 



his has its maximum value, unity, when v u. 

 An examination of equation (1) will, however, show that under these 



ircumstances the propelling force is zero, and that with a large propelling 

 force it is impossible to work under conditions which conduce to high 

 efficiency. 



