TM NO. 377 

 giving 



^'>^^-^i^./-0. (A-5) 



dtf f^t dt^x 



•Ui 



From conditions (A-3), the time derivative of U- is zero, producing the homo- 

 geneous equation: 



Solving equation (A-6): 



oj'- IC5 e ^ s (A-7) 



■where Ko is an integration constant. Substituting this in equation (A-^) yields 

 the complete solution: 



CU r l<i e "^"^H- ^W- (A-8) 



At time t=0, from the initial conditions (A-3), one can evaluate: 



K3 = - ^ Up . (A-9) 



Thus: • ^-6 



This is the general solution of (A-2), which contains the sum of the transient 

 and steady statelsnlutions . 



It is evident that: 



LIM CoM^ ^Ot -^T • (A-11) 



For steady flow, the frequency of the impeller is directly proportional to the 

 linear speed Uj>, This important property is borne out by the calibration 

 cturves of the three ducted meter systems in figures II-5, II-9j and 11-20. 



A-2 



