where 



U = velocity of fluid relative to object 



d = characteristic dimension of object 



M = dynamic viscosity 



V = kinematic viscosity 



p = fluid density 



As the Reynolds number increases, vortexes ai'e produced and shed behind 

 blunt bodies such as cylinders. When R is between 10 and 40, stationary vortexes 

 are formed. Stable and well-defined vortex patterns are carried away or shed for R 

 between 40 and 150. The line of separation moves back and forth, and transverse 

 forces appear which change direction with time. Using the Strouhal number, which 

 is nondiraensional and determined experimentally, the frequency can be found by 

 the formula'^'* 



, SU 



f =- (23) 



where 



d = diameter of body 



/ = frequency of oscillation 



U = velocity 



S = Strouhal number 

 As R is increased from 150 to 10^, the shedding becomes irregular. 



SHALLOW-WATER APPLICATION 



Considered so far have been objects in a steady-fluid flow, or objects 

 moving at fixed velocities through a still fluid, after equilibrium has been reached. 

 In the shallow-water case, however, oscillating flows are present because of wave 

 action. This motion means that fluid acceleration is present which also influences 

 the coefficient of drag, ^^'^^ the wake formation. 1^ and the apparent mass increase, 

 which is called virtual, or added mass.^^"^^ 



Of prime importance are the variations in drag coefficient and mass coeffi- 

 cient with fluid acceleration. This problem has been studied theoretically and 

 experimentally for unidirectional accelerated motions, arbitrary motions, and 

 sinusoidal oscillations. Keulegan and Carpenter^^ give a good review of these 

 references, and present results of sinusoidal fluid oscillations for cylinders and 



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