Johnson, Jr. 



EFFICIENCY 



In Ref. (2), expressions are derived for the efficiency of waterjet propulsion 

 systems strictly on the basis of momentum theory. No account is taken of (1) the 

 wake inflow to the inlet (inflow is assumed to be uniform at the velocity of the 

 craft), (2) the effect of the inlet on the resistance of the craft, and (3) the addi- 

 tional drag of the craft that may be attributed to the additional weight require- 

 ments of a waterjet system. Typical waterjet systems are schematically shown 

 in Fig. 1. 



^^^-^ 



V 

 o 



(a) 



rJrT'^^:^^ 



(b) 



■r Or-r^ -^'j 



Fig. 1 - Geometric configuration 

 of waterjets 



As derived in Ref. (2), the ratio of propulsive efficiency 17 to pump effi- 

 ciency 7] is presented in Fig. 2 as a function of the parameter h* = l^W^ ^ , 

 where h is the head added by the pump and Vq is the forward speed of the craft. 

 The various curves shown in Fig. 2 are for different values of the parameter k , 

 where the internal losses h^ (inlet, internal diffusion, ducting and nozzle) are 

 defined as h^ - Y.V^'^/2?,. The important point to note from Fig. 2 is that an 

 optimum value for h* exists for each value of K . 



Physically, Fig. 2, points out that for a given value of k , the efficiency is 

 less than optimum for h* < H* , because excess energy is used in overcoming 

 the internal losses; whereas operation at values of h* > H* ^ results in de- 

 creased efficiency because of excess kinetic energy expended in the jet. It is 

 important to recognize that operation at increasing values of h* means in- 

 creased jet velocity and consequently, for a given thrust requirement, decreased 

 discharge. Thus, operation at higher values of h* means smaller inlets, ducts, 

 pumps, and nozzles, and thus less weight for a given thrust. This fact, as is 

 pointed out in several Refs. (1 -4), generally leads the designer to select 

 H* > H*pt in order to achieve a system which requires less power to propel a 

 given payload, even though the "momentum" efficiency as presented in Fig. 2 is 

 less than optimum. 



1046 



