Flow rate‐pressure gradient measurements in periodically nonuniform capillary tubes

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Abstract
Flow rate‐pressure gradient measurments have been performed on 15 different test capillary tubes, each of which consisted of short, alternating segments of two different diameters. The Reynolds number range covered extended from 2 to 700, based on the conditions in the narrower capillary segment. Darcy's law was found valid up to about Re = 30‐50, whereas the Forchheimer equation described the data over the entire range of Re covered. The Forchheimer equation has been obtained from a nondimensional form of the volume averaged momentum equation by using the averaging theorem due to Slattery and to Whitaker. The parameters α and β have obtained precise hydrodynamic definitions. The experimental data have been treated in terms of the Forchheimer equation: the parameters α and β have been calculated using various definitions for the area of flow. Dimensionless permeability, equal to the ratio of measured‐to‐Poiseuille permeability has been found to be a minimum‐type function of small‐to‐large capillary diameter ratio. Dimensionless inertial parameter β* has been found to be a maximum‐type function of the capillary diameter ratio, if the calculation was based on the area of flow equal to the cross sectional area of the narrower capillary segment, in every case. The maximum occurred at the same value of the capillary diameter ratio as the minimum for the dimensionless permeability.