upon shape and orientation but varies considerably with the viscous char- 

 acteristics of the motion. 



Reynolds (1883) showed that the influence of viscosity depends upon 

 the dynamic viscosity of the fluid (jJ.) , the fluid density (p,), the size 

 of the body (D), and the mean velocity of the relative motion (V). Reynolds 

 combined these parameters as a dimensionless ratio called the Reynolds 

 number < K e ): VD 



where V is the kinematic viscosity of the fluid and is equal to /Li/pf 

 The magnitude of the Reynolds number indicates the relative significance 

 of inertial (VD) and viscous (V) forces affecting the motion. 



According to Rouse (1938) viscous action may produce three essentially 

 different types of resistance: deformation drag at very low Reynolds numbers, 

 with the effects of viscous stress extending a great distance into the 

 surrounding flow and causing a more or less widespread distortion of the 

 flow pattern; surface drag at much higher Reynolds numbers, with appreciable 

 deformation of the flow limited to a thin fluid layer surrounding the body; 

 and form drag at still higher Reynolds numbers, arising if the form of the 

 body is such that separation of the flow from the body occurs. The form 

 of the body also determines to some extent the magnitude of the other two 

 types of resistance. Rouse (1938) concludes that the resistance to motion 

 of an immersed body depends only upon the Reynolds number characterizing 

 the motion and the geometrical form (or shape) and orientation of the body. 



Analytical determination of Newton's coefficient of resistance here 

 called drag coefficient and represented by Cp for certain basic body forms 

 has been possible only at very low Reynolds numbers. Stokes (1851) first 

 determined analytically the drag resistance on a sphere falling through a 

 fluid at very .low Reynolds numbers (R e < 0.1). Rouse (1937) rearranged 

 Stokes' relationship into a form similar to Newton's (Equation 1). 



24 „ V 2 



f = r; Ap s- (3) 



obtaining the following relationship between Reynolds number and drag 

 coefficient for very low values of R e , 



C D x R e = 24 (4) 



Oseen (1927) and Goldstein (1929) were able to extend analytically the 

 range of Stokes' relationship to approximately R e = 2. Beyond this limit 

 the study of Cq as a function of R e has remained empirical. Schiller (1932) 

 plotted the known drag coefficients and Reynolds numbers on a Cj - R e 

 diagram. Examination of Schiller's diagram shows C/p to be solely a function 

 of R e up to very high values (R e = 5,000 for discs and R e = 500,000 for 

 spheres) . 



