TR No. 22 
The angular velocity of the impeller also consists of a constant 
plus a time varying component: 
/ 
By Si Za), (7) 
/ 
Since u' is assumed small with respect to U,@ can also be assumed 
small with respect to S23; and K (u, &’) can therefore be expanded in a 
Taylor series about the equilibrium value, zero: 
" IK 
Ki os) = 1K (aw) en ie we 22k iw! 
ee lbh i ZAMS) 
Bak 12 , O2K Free eK ay 
yl ele acre Syl eso 
U i) BIEN 15, 
The coefficients of the linear and second order terms in the series are 
1g (U, Ww) | mek, 
sp. 
(9) 
Seg = oeU fer) + an 
i ES SNe. L282 o \eyice 
se (10) 
C O a) Z ey 
=) T 
6 
OK 
ae 2 Golo oe eu = Coy 
Caine uy (11) 
A2K (y OAs) (12) 
ee) DEH)| LA we, =e 
out Sy To 
ae ee sar 
A=2 0 
