Stop Distance and Stokes Number

Note that all the variables of the system have been combined in the dimensionless group xuq/L, which is called the Stokes number (St)  

Note that the Stokes number is the ratio of the particle stop distance sp to the characteristic length of the flow L. As particle mass decreases, the Stokes number also decreases. A small Stokes number implies that the particle is able to adopt the fluid velocity very quickly. Since the dimensionless equation of motion depends only on the Stokes number, equality between two geometrically similar flows indicates similarity of the particle trajectories. 

Let us consider a particle moving with a speed f/ in a stagnant fluid with no forces acting on it. The particle will slow down because of the drag force exerted on it by the fluid and eventually stop after moving a distance Sp. We can calculate this stop distance of the parti- 

Let us try to write the equation of motion (8.37) without the gravitational term, in di-  

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