The Transfer Function 



The sample problem of this section is in the form of the flow across a 

 moving cascade. The static pressure rise across such a cavitating cascade 

 is a function of the upstream pressure and the upstream flow velocity. In 

 the absence of fluid losses, an infinitely long cascade has no change in 

 pressure rise with inlet pressure for a steady flow. An unsteady flow is a 

 different matter, however, and the component, z...., may not be expected to 

 be zero. The fluid losses in steady flow are due primarily to mixing 

 caused by the drag due to cavitation. This "momentum" loss increases with 

 decreasing pressure, and thus, we may expect quasi-steady cascade experi- 

 mental data to show a positive value of z 1 -. . Pump cascades, as sketched in 

 Figures 36 and 37, create a static pressure rise through diffusion of the 

 relative velocity. This pressure rise decreases with increased axial 

 speed (and thereby reduced angle of attack) so that on a qua si- steady basis 

 we may expect the term z to be negative, i.e., a fluctuating increase in 

 flow should result in a fluctuating decrease in pressure rise. Additional 

 complex terms may be expected in unsteady flow. 



We have repeatedly focused attention on the volume change of cavita- 

 tion with pressure; the rate of volume change is seen to be proportional to 

 the differences of down and upstream speed across the cascade. From 

 experience with steady cavitating flows, we expect the volume of cavita- 

 tion to increase with a decrease in upstream pressure, and to increase with 

 an increase of angle of attack or a decrease in inlet flow velocity. We 

 expect that, for vanishing frequency, the terms z and z „ will both be 

 negative and imaginary, and proportional to frequency, as this is the 

 appropriate behavior in the quasi-steady limit. The term z„.. is of 

 particular interest; it is related to what has been termed the "compliance" 

 by hydraulic system analysts. The compliance is the negative rate of 

 change of cavity volume with pressure. In fact, in dimensional units, z„.. 

 is equal to the negative of this compliance times jco divided by the pump 

 inlet area. It is an important system parameter, since the period of an 

 inlet pipe line oscillation is proportional to the square root of the 



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