considered constant. For this case the actual force must be given by both 

 terms of equation (24), 



dU 



(30) 



where 



K^ = 1/4 (C\, p TT c?^' = constant 



As before, let the true velocity be given by 11 = Uq + U^ sin 9 and the actual 

 output be linear with force. 



Thus 



e^K^Ks^ +K2K3U\U\ 



(31) 



Since the inertia term is still assumed negligible, equation (28) is again used to 

 solve for the indicated velocity, resulting in 



[i, = . 



1 /„ dU 



dt 



Vi 



(32) 



And Uj can be found. 



TJ,-^ I u,de 



(33) 



This method will notjiormally give the correct mean value Uq when LJq ^ 0. As 

 examples, values of Uj as found by numerical integration for two cases of Uq/U„ 

 are shown below. 



The values of /\j =0.54 and R'2 = 0.31, obtained earlier for the typical 

 example L/^, = 10 centimeters per second, T = 10 seconds, d = 0.51 centimeter, 

 were used. 



36 



