MATHEMATICAL ANALYSIS OF VISCOSITY AND REABSORPTION ON URINE FLOW THROUGH A STRAIGHT NARROW TUBE

This study investigates the effect of variable viscosity (exponential and linear) and constant reabsorption for the urine flow through a narrow tube. The inertial free flow of viscous fluid has been governed by the momentum and mass conservation through the cross-section of axisymmetric tube. The governing partial differential equations have been simplified with the help of stream function and stress components with exponential and linear variable viscosity. The resulting partial differential equations have been solved by the inverse method and give the explicit expressions for velocity, pressure, shear stress, flux and leakage of flow. It has been observed that flow in transverse direction increases with the increase in reabsorption velocity at wall, whereas horizontal flow, shear stress and volume flow rate become slow with the increase in uniform reabsorption velocity. Effect of viscosity is significant near the walls of tube because the axial velocity accelerates by increasing viscosity parameter due to the pressure gradient near the center of tube but it decelerates near the walls of tube due to surface friction. Also, the special case of variable viscosity is discussed by assuming the linear type of viscosity. The derived data for the velocity and flow rate have been used to measure the fractional reabsorption in proximal tube with varying viscosity near the wall.

Modified Reynolds Equation for Steady Flow Through a Curved Pipe

A Reynolds equation governing the steady flow of a fluid through a curvilinear, narrow tube, with its derivation from Navier–Stokes equations through asymptotic methods is presented. The channel considered may have a rather large curvature and torsion. Approximations of the velocity and the pressure of the fluid inside the channel are constructed by artificially imposing appropriate boundary conditions at the inlet and the outlet. A justification for the approximations is provided along with a comparison with a simpler case.

A synopsis of Thyrsacanthus (Acanthaceae) in Argentina and Paraguay, with notes on generic delimitation, a new combination, and lectotypifications

A taxonomic synopsis of the members of the re-circumscibed Thyrsacanthus from Argentina and Paraguay is presented. Two species are recognized for the region, T. boliviensis and T. sulcatus. The latter is a new combination here proposed, based on Jacobinia sulcata (until now treated in Carlowrightia), that is corroborated by morphological data and geographic distribution as well as molecular phylogenetic information. Thyrsacanthus sulcatus is clearly distinguished from T. boliviensis by its small, white, lilac or pale blue, presumably psychophilous flowers with a narrow tube, instead of the large and red ornithophilous flowers with a tube that widens to the throat, which is typical of other species of Thyrsacanthus. Differences between the re-circumscribed Thyrsacanthus and other genera of the Tetramerium lineage to which it belongs are discussed, and references to additional genera of Acanthaceae that present similar wide diversification in floral morphology are noted. The synopsis includes a key, full synonymies, descriptions, illustrations, distributions, and lists of representative specimens. Lectotypifications are provided for the following names: Anisacanthus malmei, Dianthera sulcata, Jacobinia caducifolia, Schaueria caduciflora, and Siphonoglossa gentianifolia.