Hydrodynamic Pressure on a Dam During Earthquakes

A straightforward analysis involving Fourier cosine transforms and the theory of Fourier seies is presented for the approximate calculation of the hydrodynamic pressure exerted on the vertical upstream face of a dam due to constant earthquake ground acceleration. The analysis uses the “Parseval relation” on the Fourier coefficients of square integrable functions, and directly brings out the mathematical nature of the approximate theory involved.

Extrapolation and series acceleration procedures: Hard spheres and discs as illustrations

Three new procedures - in the context of estimation of virial coefficients and summation of the partial virial series for hard discs and hard spheres - are proposed. They are based on the parametrised Euler transformation, a novel resummation, identity and the ε-convergence methods respectively. A comparison with other estimates (molecular dynamics, graph theory and empirical methods) reveals satisfactory agreement.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

CFD Analysis of conjugate natural convection in a vertical annulus

Conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. A parametric study is performed by varying the Grashof number, aspect ratio, and the solid-to-fluid thermal conductivity ratio over wide ranges with the Prandtl number fixed at 0.7. Results are presented for the variation of several quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number, and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The average Nusselt number from the conjugate analysis is found to be between the Nusselt numbers of the isothermal and the isoflux cases. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. Correlations are presented for the Nusselt number and the dimensionless temperatures of interest in terms of the parameters of the problem.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Axial heat conduction effects in natural convection along a vertical cylinder

MANY TRANSPORprTo cesses occur in nature and in industrial applications in which the transfer of heat is governed by the process of natural convection. Natural convection arises in fluids when the temperature changes cause density variations leading to buoyancy forces. An excellent review of natural convection flows has been given by Ede [I]. Recently, Minkowycz and Sparrow [2, 31, Cebeci [4], and Aziz and Na [S] have studied the steady, laminar, incompressible, natural convection flow over a vertical cylinder using a local nonsimilarity method, a finite-difference scheme, and an improved perturbation method, respectively. However, they did not take into account the effect ofaxial heat conduction for small Prandtl number. It is known that the axial heat conductioneffect becomesimportant for low-Prandtl-number fluids such as a liquid metal.

Perturbation expansions and series acceleration procedures: Part-II. Extrapolation techniques

Three new procedures for the extrapolation of series coefficients from a given power series expansion are proposed. They are based on (i) a novel resummation identity, (ii) parametrised Euler transformation (pet) and (iii) a modifiedpet. Several examples taken from the Ising model series expansions, ferrimagnetic systems, etc., are illustrated. Apart from these applications, the higher order virial coefficients for hard spheres and hard discs have also been evaluated using the new techniques and these are compared with the estimates obtained by other methods. A satisfactory agreement is revealed between the two.

Velocity and acceleration analysis of complex mechanisms by graphical iteration

A simple graphical method is presented for velocity and acceleration analysis of complex mechanisms possessing low or high degree of complexity. The method is iterative in character and generally yields the solution within a few iterations. Several examples have been worked out to illustrate the method.

Unsteady nonsimilar natural convection over a vertical flat plate in a thermally stratified fluid

Abstract is not available.

Free convection heat transfer to mercury in vertical annuli

Data on free convection heat transfer to water and mercury are collected using a test rig in vertical annuli of three radii ratios, the walls of which are maintained at uniform temperatures. A theoretical analysis of the boundary layer equations has been attempted using local similarity transformation and double boundary layer approach. Correlations derived from the present theoretical analysis are compared with the analysis and the experimental data available in literature for non-metallic fluids and also with the present experimental data on water and mercury. Generalised correlations are set up for expressing the ratio of heat transferred by convection to the heat transferred by pure conduction and Nusselt's number, in terms of Grashof, Rayleigh and Prandtl numbers, based on the theoretical analysis and the present data on mercury and water. The present generalised correlations agree with the reported and present data for non-metallic fluids and liquid metals with an average deviation of 9% and maximum deviation of ± 13.7%.

Water-wave scattering by two submerged plane vertical barriers-Abel integral-equation approach

The classical problem of surface water-wave scattering by two identical thin vertical barriers submerged in deep water and extending infinitely downwards from the same depth below the mean free surface, is reinvestigated here by an approach leading to the problem of solving a system of Abel integral equations. The reflection and transmission coefficients are obtained in terms of computable integrals. Known results for a single barrier are recovered as a limiting case as the separation distance between the two barriers tends to zero. The coefficients are depicted graphically in a number of figures which are identical with the corresponding figures given by Jarvis (J Inst Math Appl 7:207-215, 1971) who employed a completely different approach involving a Schwarz-Christoffel transformation of complex-variable theory to solve the problem.