TM No, 377 



from the impeller frequency-time plot as the time required to reach about 

 63 percent of the final frequency value. Four estimates were made of the 

 time constant , involving both directions of the u and w meters. The results 

 were essentially identical. 



The impeller bearings were dry during the wind tunnel test. This may 

 result in an added frictional drag, tending to lengthen the response time. 

 The impellers in water are constantly lubricated, which certainly contri- 

 butes to their overall sensitivity to oscillatory flow. 



The dynamic response time of the impeller system in sea water (desig- 

 nated by T w ) can be estimated by utilizing a principle of dynamic simi- 

 larity. The time constant T is given in appendix B as : 



where I is the moment of inertia, and K_ is the constant of proportionality 

 relating resistance to the drag forces That oppose the driving force produced 

 by the fluid velocity u= 



The law of dynamic similitude can be used to estimate the value of Ty. 

 Since the moment of inertia I of the impeller is independent of its sur- 

 rounding medium., equation (A-12) can be rewritten: 



% K W " T A K A> (II . 25) 



or T W = t aVV 



where the subscripts W and A represent the water and air media, The next- 

 problem is to determine the ratio of the constants K^/k . Since the K's 

 are,, in a sense, drag coefficients of the impeller^ they are related to the 

 impeller interaction with the fluid medium. They should be a function,, 

 therefore, of the fluid density £> , the kinematic viscosity,/* f and a 

 dimensional scale X „ Setting K» equal to a function of density P , some 

 scale factor A associated with the impeller dimensions; and the dynamic 

 viscosity y {=/$*/) } and using methods of dimensional analysis (see 

 Bridgeman, 1956): 



k= q eS B f i en- 26 ) 



2 ^ 



where Q is a dimensionless constant 8 Since the units of K are M L T 

 (where M = mas£ 5 L « length, and T = time) ? the exponents A., B s and C can 

 be evaluated: 



K= Q f°7'A 3 = 0j\ s . (II _ 27) 



The ratio of the values K for air and sea water (K A /Ky), which is needed 



to solve for T in equation 11-25, is given by: 

 w 



1+0 



