Fluid Mechanics

Given that the terminal velocity of a sphere falling in a viscous fluid is given by Stokes' law: Where: - is the terminal velocity, - is the radius of the sphere, - and are the densities of the sphere and the fluid respectively, - is the acceleration due to gravity, - is the coefficient of viscosity of the fluid. ### Step 1: Set up the equation for both spheres. For sphere 1: For sphere 2, with terminal velocity : ### Step 2: Relate the two equations. Dividing the second equation by the first equation: This simplifies to: Thus, Taking the square root of both sides: Therefore, Thus, is of .