Equations of fluid flow in capillaries under pressure gradient: A discussion on applicability and interrelations

Applying the overall friction forces concept that resistance to flow depends on the kinetic energy density and fluid–solid contact area, a general equation has been derived for fluid flow through capillaries. For laminar regime, the friction coefficient f has been assumed inversely proportional to a Reynolds number with a specific proportional constant a* depending on the shape of the capillary (circular, rectangular, or any other form). For specific values of a*, the general equation assumes specific forms for gas and liquid flow through capillaries of different shapes. Average gas pressure in the capillary during gas flow has been defined in a more justified way than that in literature till date. It is suggested that in order to make the liquid and gas flows through a given capillary mutually predictable, the gas viscosity could not be considered a constant, rather a function of the average pressure and hydraulic diameter of the capillary.