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How to calculate particle settling velocity - tube settlers I Stokes law

Stokes law - Physics of particle settling

About the blog

Karl-Uwe Schmitz
Karl Schmitz is a consultant and sales agent for FBBR, diffused air and lamella system solutions. We are working together with the lead manufacturers for drinking water and waste water components in the United States.
Schneider Electric

In 1851 George Gabriel Stokes defined how drag forces effect spherical objects in a viscous fluid in the formula: Fd = 6pi * u * R * v.

An object in a viscous fluid like water always experiences a downward force – because of its weight and gravity – as well as an upward force. The upward force equals the weight of water which was displaced by the object. Furthermore, a floating object will collide with other particles on its way to the water surface. So, the downward forces must be added by drag forces as a consequence of these collisions. Just like that, a settling object, will experience additional upward drag forces. The object has to face further drag forces - caused by the viscosity and the flow velocity of the fluid relatively to the object.

A fluid with a high viscosity like honey makes it much more difficult for a particle to settle down. At the same time, objects within a fluid with a high flow velocity will be dragged into the flow direction. Both the viscosity and flow velocity are expressed in Strokes law. - R is the radius of the object in the water. Therefore, D in the formula U = W + D can be replaced by Fd for drag forces.

As Stokes law is only applicable for spherical objects the formula can be added by a form factor for different object geometries. Strokes law plays a very important role in the water and waste water industry e.g. to determine the size of settling basins and for the calculation of lamella clarifiers. 


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