Consider a catalyst, specific gravity 1.75, in a bed with air flowing upward through it at 650 K and an average pressure of 1.8 atm (μ_air = 3 × 10^-5 kg/m s). The catalyst is spherical with a diameter of 0.175 mm. The static void fraction is 0.55, and the void fraction at minimum fluidization is 0.56. The slumped bed height is 3.0 m, and the fluidized bed height is 3.1 m.

Calculate the minimum fluidization velocity.

Calculate the pressure drop at minimum fluidization.

Estimate the pressure drop at one-half of the minimum fluidization velocity assuming incompressible flow.