Propagation of one-dimensional unloading waves in materials exhibiting yielding delay phenomena

Summary The nature of possible unloading waves in materials exhibiting yielding delay phenom ena has been discussed in this paper. The differential equation governing the propagation of the waves, has been solved by this method of characteristics. In this case also as in materials not exhibiting yielding delay phenomena, the unloading wave propagates with the velocity of elastic waves, if it is a wave of discontinuity, and if the load is suddenly increased the unloading wave travels with plastic wave velocity.     

Reinvestigation on mixing length in an open channel turbulent flow

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sediment-laden turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels. The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.     

On similarity solution of an unsteady laminar boundary layer along a flat plate

Summary A unified analysis has been made to obtain all possible similarity solutions of the steady and unsteady, forced flow, inside a boundary layer along a flat plate. Though previously, attempts were made to obtain similarity solutions of a steady boundary layer flow neglecting viscous dissipation term in the energy conservation equation but the treatments were not complete. Here we have taken account of the viscous dissipation term. In the steady case it has been shown that for a similarity solution of both velocity and temperature, there should be a relation between the undisturbed flow outside the boundary layer and the temperature of the plate. It has been shown that the similarity solution exists in the unsteady case if we neglet the viscous dissipation term in the energy equation.     

A generalized method of solution of unsteady incompressible boundary layer theory

Summary In the present paper, a generalized method of solution of the problem of incompressible, unsteady, laminar boundary layer flow with the main-stream velocity of the formX(x) N(t) is developed. In many practical problems, the external velocity potential may be given in the above separable form, from theoretical and or experimental considerations.Presented in the Advance Level Winter Workshop in Fluid Dynamics, 1970, I.I.T. Delhi, India.     

Slow motion of a viscous conducting fluid past ellipsoids in the presence of a toroidal magnetic field

Summary An attempt has been made here, to obtain solutions for the velocity and magnetic field, for a flow past an ellipsoid, in the presence of a toroidal magnetic field, when magnetic Reynold number and Hartman number are small.     

Unified solution of the unsteady boundary layer equations

Summary The momentum conservation equation for a compressible boundary layer flow, may be transformed to the corresponding equation for the incompressible flow, in some cases, and the resulting equation can be solved by series expansion.     

Flow past spheres and spheroids in the presence of a toroidal magnetic field

Summary Stewartson [1]²) has considered the inviscid flow past a sphere in the presence of a uniform magnetic field andMurray andLudford [2] have investigated a similar problem in which the magnetic field originates from an axially symmetric dipole field situated at the centre of the sphere. In connection with the study of earth's magnetic field, the toroidal part of this field plays a dominant part. This gives rise to the importance of studying the effect of a toroidal magnetic field on flows past different bodies of revolution; specially past spheres and spheroids. In the present note inviscid flows past a sphere, and a spheroid, are considered, for the case of a toroidal magnetic field originating in the fluid. In the case of the sphere the field inside the sphere consists of an electric dipole directed along the axis of symmetry together with a uniform electric field which produces a uniform current along the axis. In the case of the spheroid, the field inside it is due to an electric dipole and quadrupole directed along the axis of symmetry, together with a uniform electric field which produces a uniform current along this axis.     

Theory of dispersion of solutes in non-Newtonian flows through a circular tube

Summary In the present paperTaylor's analysis of the dispersion of a soluble matter in Newtonian flow through a circular tube is extended in the case of non-Newtonian flows of Eyring and Reiner-Philippoff model fluids. It has been shown here that the results for the Newtonian fluid can be deduced from the corresponding results of both the two types non-Newtonian flows. Few specific cases of both the two types of fluids have been studied. Aris modification ofTaylor's analysis is also applicable to non-Newtonian flows discussed here. The results may be useful in connection with the study of the dispersion of soluble salts in blood vessels. It may also be useful to physicians who wish to study molecular diffusion coefficients.     

A mathematical model on depth-averaged <Emphasis Type="Italic">β</Emphasis>-factor in open-channel turbulent flow

The well-known Rouse equation is the most widely used equation to determine the vertical distribution of suspended sediment concentration in an open-channel flow. The exponent of Rouse equation, known as Rouse number, contains the parameter β defined by the ratio of sediment diffusion coefficient to turbulent diffusion coefficient. As such to measure sediment concentration accurately, an appropriate expression for β is essentially needed. The present study, therefore, focuses on the derivation of depth-averaged β through modified expressions of sediment and turbulent diffusion coefficients. A regression analysis is done to establish the relation between β and normalized settling velocity, and the relation is used to determine suspension concentration.