Motion of Sphere in a Medium

To come to a more important item for chemists, we derive Stokes law by means of dimensional analysis. A sphere with radius r is moving with constant speed v in a viscous medium with viscosity rj subjected to a constant force F. We assume that a steady velocity will be established. This velocity is dependent on the force acting on the sphere, on the radius of the sphere, and on the viscosity that is surrounding the sphere. The physical dimensions of the variables are 

Using a similar procedure like in the pendulum example, we obtain 

Note that one variable, here r, can occur without an exponent, since the equation system will be homogeneous. Rearranging, we arrive at 

Further, observe that K may be a function of a dimensionless quantity. Dimensional analysis gives no information about the coefficient K. It is interesting to find that in the limiting cases oi F 0, K seems to be a constant. If there is no force, then we put U = 1 in the law. There is no solution available, say a movement with constant velocity. 

There may be also other solutions of the problem. We are doing now a rather stepwise heuristic approach. The individual steps are shown in Table 11.6. First, 

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