f 



TM NO. 377 



Referring to chapter II, the ducted meter is subjected to a step input of 

 velocity Um at a point in time where : 



t = I- = T^ , (A-12) 



Kl 



In equation (A-10) 60 (t) can be evaluated^ utilizing (A-ll)^ as: 



U) (t) =W^ = ^ Up (H) = 63^ H " (A=13) 



Kl Kl 



The value Tj. s i/ktl is defined as the response timeo Likewise^ T"-'- (seC^) 

 may be defined as the frequency response » Generally speaking, the instrument 

 is incapable of registering fluctuations in flow greater than 1^°^ cpSo The 

 dividing line is completely arbitrary ;, However^ for CMDXM III, having T = 

 6C ■ milliseconds, this response time is surely small enough to observe fluctu- 

 ations due to surface waves ^ich are of the order of 3000-4000 milliseconds. 



Response to a Sinusoidal Input =■" The next step is to examine the response 

 characteristics of the ducted meter to a sinusoidal driving function, which 

 might be cmdely compared to a single Fourier con^onent of an ocean wave. 



One can assume the same equation of motion given in equation (A-2), except 

 that u is given as a siniisoidal function. Thus, instead of (A-2); 



g + I%£J ^ ]% cosJIto (A"li^) 



The JLis the driving frequency given by ^TT Tp"* j vhereTpis the period of the 

 forcing function on the right hand side of (A-l^i-). 



Letting K^/l ==_flo, the auxiliary equation becomes: 



W = A e " -^'''^ . (A-15) 



It is assumed that A-A(t) can serve as part of the solution to equation (A=l4). 

 Substituting (A»15) into (A-14)j with the necessaiy adjustment, gives : 



(A-16) 



A»3 



