OM NO. 377 





or siEtply 



(A-28) 





Dividing (A-28) by €/^ and multiplying both sides of the equation by the respec- 

 tive conrplex conjugates gives: 



Taking the liMt of (A-29) as c/Vi^o , we have from equations (A-25) and (A-26) : 



Equation (A-30) gives the relation between the spectra of quasi-random function 

 u(t) aaid the spectrum of impeller rotatio3ial response ^ (t). 



'Ihe next relationship to be examined is between the auto-covariance functions 

 of both the turbulent velocity fluctuations u(t) and the impeller response 

 function LO (t). In order to compare the response of each function at an instant 

 T and at a later time 7* , we mxist determine the relation between the auto- 

 covariance functions given by: 



4>Ur) * ^L't)'^iirt7) (A.31) 



and 



4>^(.i) = <^(^) t^C-^-^f) - (A-32) 



ISiese functions are defined in chapter III. 



It is relation (A°32) that is actually measured. From this, (A-31) is inter- 

 preted and the spectrum function ^0^) inferred* From equations (A-I5) aJid 

 (A-16), and the properties (A-I8) and (A-I9) : 



A-6 



