CHAPTER
10
When a particle moves steadily through a fluid, there are two principal forces acting upon it, the external force causing the motion and the drag force resisting motion which arises from frictional action of the fluid. The net external force on the moving particle is applied force less the reaction force exerted on the particle by the surrounding fluid, which is also subject to the applied force, so that
where F_{s} is the net external accelerating force on the particle, V is the volume of the particle, a is the acceleration which results from the external force, r_{p} is the density of the particle and r_{f} is the density of the fluid. 
The drag force on
the particle (F_{d}) is obtained by multiplying the velocity pressure
of the flowing fluid by the projected area of the particle
where C is the coefficient known as the drag coefficient, r_{f} is the density of the fluid, v is the velocity of the particle and A the projected area of the particle at right angles to the direction of the motion. If these forces are acting on a spherical particle so that V = pD^{3}/6 and A = pD^{2}/4, where D is the diameter of the particle, then equating F_{s} and F_{d}, in which case the velocity v becomes the terminal velocity v_{m}, we have:
It has been found, theoretically, that for the streamline motion of spheres, the coefficient of drag is given by the relationship:
Substituting this value for C and rearranging, we arrive at the equation for the terminal velocity magnitude This is the fundamental equation for movement of particles in fluids. Mechanical separations > SEDIMENTATION Back to the top 
