A packed bed reactor design is proposed which uses downward flow through a 6.0 m long bed which is packed with 12.0 mm diameter spherical particles. The diameter of the (cylindrical) bed (perpendicular to the flow) is 2.0 m, and the solidity of the bed is 0.61.

The pressure head at the inlet to the column (where QIN enters in the diagram below) is 42.0 m (H2O); the pressure head at the outlet (where QOUT exits in the diagram below) is 5.0 m (H2O). The process fluid has a specific gravity of 1.05 and a viscosity of 1.4 centipoise.

Determine the volume flow rate passing through the bed under these conditions.