On the Derivation of Pressure Field Distribution at the Entrance of a Rectangular Capillary

In capillary flow, integral momentum approach is used to derive the governing equation, which requires an expression for the pressure field at the inlet of the capillary. Generally, the pressure field for circular capillary is deduced with hemispherical control volume. This expression has been extended for other noncircular capillaries with an equivalent radius approximation. In case of high aspect ratio channels, the semicylindrical control volume needs to be considered. In the present study, the correct expression for the entrance pressure field for high aspect ratio capillaries is derived with such appropriate control volume. [DOI: 10.1115/1.4001641]