Viscous drag and secondary flow in granular beds

Departure from Darcy's law in the flow of fluids through granular beds can be interpreted as due to a regular secondary flow being set up. That view is supported by reference to White's experiments on helically wound tubes, and by reference to recent experiments on the flow of viscoelastic liquids through granular beds. Experiments are here described which establish a single non-dimensional curve to describe the results of the flow of air and of liquids through granular beds of spheres and of irregular particles. The model of a granular bed is discussed and experiments are described which establish the identity of the flow through helices with that through the same cylindrical tubes bent into coplanar S shapes. An equation is given relating the resistance of a granular bed to the flow through it when Darcy's law is no longer applicable.