where Vi Is the velocity at t = t-. , and Cq Is the appropriate coefficient of drag. 

 After a given time the velocity of the falling body attains a terminal velocity, V-r, 

 in which condition the drag force balances the body weight minus the buoyancy force; 

 i.e., 



where (Cq) is the coefficient of drag at the Reynolds number corresponding to a 

 velocity of Vj . Equation D-5 may be rewritten as 



The function f (Vi-L/ju) is not known and cannot be defined analytically, and 

 Equation D-6 cannot be solved explicitly for the terminal velocity, Vt , without 

 the prior assumption of a particular Crj . 



However, starting from zero initial velocity, it is possible to determine the 

 motion of a particular body by considering the acceleration and velocities attained 

 over small increments of time. A simple computer program was written to accomplish 

 this. At t = the velocity is zero, there is no drag force, and the body will accel- 

 erate under the force (Wn -Fn). At t = t] the velocity is finite and the appropriate 

 Reynolds number may be calculated together with the corresponding Cr^ . For the 

 purpose of these calculations, Cq was specified at increments of Rg , and a simple 

 interpolation was made to determine the specific Cr^ corresponding to Rg at t = tp 

 Hence the drag and out-of-ba lance force may be calculated at t = t-j together with 

 the instantaneous acceleration at this point. The process can be repeated to deter- 

 mine the velocity of the body at time increments from t = to t = T, where T is the 

 time taken to attain a terminal velocity. 



For an up-to-date complete treatment of hydrodynamic drag, the excellent 

 treatise prepared and published by Dr. Sighard F. Hoerner^ should be consulted. 



71 



