text: The Archimedes number is applied often in the engineering of packed beds, which are very common in the chemical processing industry. A packed bed reactor, which is similar to the ideal plug flow reactor model, involves packing a tubular reactor with a solid catalyst, then passing incompressible or compressible fluids through the solid bed. When the solid particles are small, they may be "fluidized", so that they act as if they were a fluid. When fluidizing a packed bed, the pressure of the working fluid is increased until the pressure drop between the bottom of the bed (where fluid enters) and the top of the bed (where fluid leaves) is equal to the weight of the packed solids. At this point, the velocity of the fluid is just not enough to achieve fluidization, and extra pressure is required to overcome the friction of particles with each other and the wall of the reactor, allowing fluidization to occur. This gives a minimum fluidization velocity, , that may be estimated by:
  where:
  *  is the diameter of sphere with the same volume as the solid particle and can often be estimated as , where  is the diameter of the particle.