On slip of a viscous fluid through proximal renal tubule with linear reabsorption

<p>The hydrodynamical problem of flow in proximal renal tubule is investigated. Axisymmetric flow of viscous, incompressible fluid through the proximal renal tubule that undergoes linear reabsorption with slip at the wall is considered. The stream function is used to transform the governing equations to system of ordinary differential equations. The analytical solutions for velocity components, pressure distribution, fractional reabsorption and the shear stress are found. The effect of slip parameter and reabsorption rate on the flow have been investigated. The points of extreme values for the axial and radial velocity components are identified. The solution is applied to physiological data from human and rat kidney, and the results are presented in tables and graphs.</p>

Circulation conservation and vortex breakup in magnetohydrodynamics at low magnetic Prandtl number

In this paper we examine the role of weak magnetic fields in breaking Kelvin’s circulation theorem and in vortex breakup in two-dimensional magnetohydrodynamics for the physically important case of a fluid with low magnetic Prandtl number (low $Pm$ ). We consider three canonical inviscid solutions for the purely hydrodynamical problem, namely a Gaussian vortex, a circular vortex patch and an elliptical vortex patch. We examine how magnetic fields lead to an initial loss of circulation $\unicode[STIX]{x1D6E4}$ and attempt to derive scaling laws for the loss of circulation as a function of field strength and diffusion as measured by two non-dimensional parameters. We show that for all cases the loss of circulation depends on the integrated effects of the Lorentz force, with the patch cases leading to significantly greater circulation loss. For the case of the elliptical vortex, the loss of circulation depends on the total area swept out by the rotating vortex, and so this leads to more efficient circulation loss than for a circular vortex.

Studies on Resonant Water Motion Between a Ship and a Fixed Terminal in Shallow Water

This work focuses on the hydrodynamical problem of a Liquid Natural Gas (LNG) carrier near a Gravity Based Structure (GBS) -type offshore terminal subject to incoming waves in medium deep to shallow water conditions. The work is restricted to 2D, and the ship is restrained from moving. The resonant behavior of the fluid in the gap between the ship and the terminal is investigated. The problem is investigated by means of a numerical model and model tests. Potential theory is assumed, and a linear as well as a nonlinear time-domain numerical wavetank based on a boundary element method with a mixed Eulerian–Lagrangian approach is implemented for this purpose. Model tests (near 2D) of a midship section near a vertical wall are carried out in a 26.5m long and 0.595m wide wave flume in model scale 1:70. In full scale the ship beam is 45m and the ship draft is 12m. The ship model is constructed in such a way as to avoid flow separation, i.e., no sharp corners. Several parameters are varied: water depth, wave period, and wave steepness. Wave elevation is measured at 12 locations.

Resonant Water Motion Between a Ship and a Terminal in Shallow Water

This work focus on the hydrodynamical problem of an LNG carrier near a GBS-type offshore terminal subject to incoming waves in medium deep to shallow water conditions. The work is restricted to 2D and the ship is restrained from moving. The resonant behaviour of the fluid in the gap between the ship and the terminal is investigated. The problem is investigated by means of a numerical model and model tests. Potential theory is assumed and a linear as well as a nonlinear time-domain numerical wavetank based on a boundary element method with a Mixed Eularian-Lagrangian approach is implemented for this purpose. Model tests (near 2D) of a mid-ship section near a vertical wall is carried out in a 26.5m long and 0.595m wide wave flume in model scale 1:70. In full scale the ship beam is 45m and the ship draft 12m. The ship model is constructed in such a way as to avoid flow separation, i.e. no sharp corners. Several parameters are varied: Water depth, wave period and wave steepness. Wave elevation is measured at twelve locations.

On waves at an interface between two liquids

In this paper it is shown that a class of linearized interface-wave problems for two superposed inviscid liquids of unequal densities occupying regions which are symmetric about the interface can be reduced to a surface-wave problem in the lower region together with a classical hydrodynamical problem for potential flow in the lower region under a plane lid. The effect of interfacial tension is included. Examples of fundamental singularities in two semi-infinite liquids are given.

Gravity currents and related phenomena

This paper presents a broad investigation into the properties of steady gravity currents, in so far as they can be represented by perfect-fluid theory and simple extensions of it (like the classical theory of hydraulic jumps) that give a rudimentary account of dissipation. As usually understood, a gravity current consists of a wedge of heavy fluid (e.g. salt water, cold air) intruding into an expanse of lighter fluid (fresh water, warm air); but it is pointed out in § 1 that, if the effects of viscosity and mixing of the fluids at the interface are ignored, the hydrodynamical problem is formally the same as that for an empty cavity advancing along the upper boundary of a liquid. Being simplest in detail, the latter problem is treated as a prototype for the class of physical problems under study: most of the analysis is related to it specifically, but the results thus obtained are immediately applicable to gravity currents by scaling the gravitational constant according to a simple rule.In § 2 the possible states of steady flow in the present category between fixed horizontal boundaries are examined on the assumption that the interface becomes horizontal far downstream. A certain range of flows appears to be possible when energy is dissipated; but in the absence of dissipation only one flow is possible, in which the asymptotic level of the interface is midway between the plane boundaries. The corresponding flow in a tube of circular cross-section is found in § 3, and the theory is shown to be in excellent agreement with the results of recent experiments by Zukoski. A discussion of the effects of surface tension is included in § 3. The two-dimensional energy-conserving flow is investigated further in § 4, and finally a close approximation to the shape of the interface is obtained. In § 5 the discussion turns to the question whether flows characterized by periodic wavetrains are realizable, and it appears that none is possible without a large loss of energy occurring. In § 6 the case of infinite total depth is considered, relating to deeply submerged gravity currents. It is shown that the flow must always feature a breaking ‘head wave’, and various properties of the resulting wake are demonstrated. Reasonable agreement is established with experimental results obtained by Keulegan and others.