unsteady flows across cavitating pump cascades, we can see that a plausible 

 form of the transfer function for a pump would be (with reference to the 

 notation of Figure 38) 



(39) 



the circumflexes, again, refer to the unsteady fluctuations. In the limit 

 of zero frequency, the steady pump performance curve must have the result 

 that 



'12 



(40) 

 tan 3 



for infinitesimal excursions about the operating point. When the frequency 

 is not zero we may expect that z and z become complex and that z and 

 z will become important 



The steady state pump test then provides limiting estimates of 

 z and z . Much of the early work on hydraulic system dynamics involving 

 cavitating pumps has been based upon the idea that the term z . is pre- 

 cisely a "compliance" effect and that z was zero. The compliance was 

 then determined by making a best fit to field data of observed system 

 oscillations (see, e.g., Rubin 1966). It was, of course, not necessary to 

 assume z to be zero except for simplicity. Later, Brennen et al., (1976) 

 showed from limiting quasi-steady arguments based on field data, that the 

 term corresponding to z was, indeed, important, and that this term, as 

 well as z , could be estimated from quasi-steady cavitating cascade theory. 

 As it turned out, these estimates, even when the effects of blade thick- 

 ness were included, underestimated the results of field observations by a 

 fair amount, particularly so for the compliance term. It had been shown 

 previously by Brennen (Brennen 1973) that the compliance effect due to 



82 



