A widely used dimensionless number, Fr, that represents the influence of gravity in the power relationship for fluid systems such as pumping, mixing in unbaffled tanks and reactors, and in determining the extent of fluidization of particles in a fluidized bed. For a fluidized bed it is expressed as:
where v is the minimum fluid velocity calculated over the entire cross-section of the bed, dp is the particle diameter (or diameter corresponding to the surface mean diameter), and g is the gravitational acceleration. Since the viscosity of gases is low, the velocity is high and aggregative fluidization occurs for Fr greater than a value of 1. Particulate fluidization occurs for Fr less than 1. For stirred tanks it is expressed as:
where D is the diameter of the impeller and N is the rotational speed in rps. It is named after British engineer William Froude (1810–79) who developed laws for the resistance of the hulls of ships in water and in predicting their stability.