Critical earthquake input power spectral density function models for engineering structures

The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

Bed Shear from Velocity Profiles: A New Approach

A new binary law of velocity distribution has been developed to describe the velocity profile for the entire flow region. The law is a combination of logarithmic law, valid in the wall (inner) region, and parabolic law, valid in the core (outer) region of the flow. The validity of the law has been established based on earlier data on flat plates, rough and smooth pipes and experimental data obtained from rigid-walled open channels with plane sand beds. A procedure of estimating bed shear stress from the proposed law of velocity distribution using the measured velocity profile has been evolved. Bed shear estimates made according to this procedure are in agreement with the values obtained from uniform flow analysis in the case of open channel flow over a sediment bed. The proposed method of estimating the bed shear stress from the observed velocity profiles is found to be particularly useful in cases where it is difficult to determine precisely the true bed level, such as in the case of flow over sediment beds.

Stream power criterion and design of sand bed channels at incipient motion

The critical stream power criterion may be used to describe the incipient motion of cohesionless particles of plane sediment beds. The governing equation relating ``critical stream power'' to ``shear Reynolds number'' is developed by using the present experimental data as well as the data from several other sources. Simultaneously, a resistance equation, relating the ``particle Reynolds number'' to the``shear Reynolds number'' is developed for plane sediment beds in wide channels with little or no transport. By making use of these relations, a procedure is developed to design plane sediment beds such that any two of the four design variables, including particle size, energy/friction slope, flow depth, and discharge per unit width in the channel should be known to predict the remaining two variables. Finally, a straightforward design procedure using design tables/design curves and analytical methods is presented to solve six possible design problems.

Analysis of gradually and spatially varied flow in sand-bed channels

Seepage through a sand bed affects the channel hydrodynamics, which in turn alters channel stability. Thus, the effect of seepage on its hydrodynamic parameters needs to be ascertained. The present work analyses spatially varied flow of a sand-bed channel subjected to seepage in the downward direction through a sand bed. Numerically calculated flow profiles affected by seepage have been verified using experimental observations. The present work also analyses the friction slope, velocity and bed shear stress variations along the channel for both seepage and no-seepage conditions. It was found that the downward seepage-induced channel flow has larger friction slope and bed shear stress than that of no-seepage.

Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Study of gas-fines in decreasing gas velocity in a packed bed

It has been well recognized now that the blast furnace aerodynamics can be represented more accurately under the decreasing gas velocity condition. Therefore, gas-fines study has been carried out in a packed bed under the decreasing gas velocity condition. Gas and fines flow equations have been developed and solved, for two-dimensional case using finite volume method. To take into account the turbulence, k-e turbulent flow model has also been developed in two-dimension. The model's predictions have been validated against the published experimental data for the increasing gas velocity case, as no experimental data are available in open literature for the decreasing gas velocity. This study shows the difference in the results for increasing and decreasing gas velocity cases under various conditions which have been reported here. Implication of the results to the blast furnace condition has also been discussed.

Transition of turbulent pipe flow

The velocity profile in turbulent pipe flow is usually divided into two regions, a wall or inner region and a core or outer region. For the inner region, the viscosity and wall shear stress are the important parameters governing the velocity distribution whereas for the outer region, the wall reduces the velocity below the maximum velocity independent of viscosity. In the present work, a velocity model is proposed for turbulent flow in the wall region of a pipe covering the entire transition from smooth to rough flows. Coupling this model for the wall region with the power law velocity model for the core region, an equation for the friction factor is obtained. The model constants are evaluated by using Nikuradse's experiments in the fully smooth and rough turbulent flows. The model shows good agreement with the friction factor and the velocity profiles obtained by Nikuradse for the transition region of turbulent flow.

Water balance modelling in a tropical watershed under deciduous forest (Mule Hole, India): Regolith matric storage buffers the groundwater recharge process

Accurate estimations of water balance are needed in semi-arid and sub-humid tropical regions, where water resources are scarce compared to water demand. Evapotranspiration plays a major role in this context, and the difficulty to quantify it precisely leads to major uncertainties in the groundwater recharge assessment, especially in forested catchments. In this paper, we propose to assess the importance of deep unsaturated regolith and water uptake by deep tree roots on the groundwater recharge process by using a lumped conceptual model (COMFORT). The model is calibrated using a 5 year hydrological monitoring of an experimental watershed under dry deciduous forest in South India (Mule Hole watershed). The model was able to simulate the stream discharge as well as the contrasted behaviour of groundwater table along the hillslope. Water balance simulated for a 32 year climatic time series displayed a large year-to-year variability, with alternance of dry and wet phases with a time period of approximately 14 years. On an average, input by the rainfall was 1090 mm year(-1) and the evapotranspiration was about 900 mm year(-1) out of which 100 mm year(-1) was uptake from the deep saprolite horizons. The stream flow was 100 mm year(-1) while the groundwater underflow was 80 mm year(-1). The simulation results suggest that (i) deciduous trees can uptake a significant amount of water from the deep regolith, (ii) this uptake, combined with the spatial variability of regolith depth, can account for the variable lag time between drainage events and groundwater rise observed for the different piezometers and (iii) water table response to recharge is buffered due to the long vertical travel time through the deep vadose zone, which constitutes a major water reservoir. This study stresses the importance of long term observations for the understanding of hydrological processes in tropical forested ecosystems. (C) 2009 Elsevier B.V. All rights reserved.

Geometrically simple linear weirs using circular quadrants

A detailed theoretical analysis of flow through a quadrant plate weir is made in the light of the generalized theory of proportional weirs, using a numerical optimization procedure. It is shown that the flow through the quadrant plate weir has a linear discharge-head relationship valid for certain ranges of head. It is shown that the weir is associated with a reference plane or datum from which all heads are reckoned.Further, it is shown that the measuring range of the quadrant plate weir can be considerably enhanced by extending the tangents to the quadrants at the terminals of the quadrant plate weir. The importance of this weir (when the datum of the weir lies below its crest) as an outlet weir for grit chambers is highlighted. Experiments show excellent agreement with the theory by giving a constant average coefficient of discharge.

A numerical study of division of flow in open channels

A two-dimensional numerical model which employs the depth-averaged forms of continuity and momentum equations along with k-e turbulence closure scheme is used to simulate the flow at the open channel divisions. The model is generalised to flows of arbitrary geometries and MacCormack finite volume method is used for solving governing equations. Application of cartesian version of the model to analyse the flow at right-angled junction is presented. The numerical predictions are compared with experimental data of earlier investigators and measurements made as part of the present study. Performance of the model in predicting discharge distribution, surface profiles, separation zone parameters and energy losses is evaluated and discussed in detail. To illustrate the application of the numerical model to analyse the flow in acute angled offtakes and streamlined branch entries, a few computational results are presented.

On the dual head-discharge characteristics of a modified chimney weir

This paper is concerned with the dual head-discharge characteristics of a modified chimney weir. It is shown by an optimization procedure that the modified chimney weir having an inward trapezoidal weir over an inverted V-notch can produce discharges proportional to both the logarithm of the head as well as the linear power of the head reckoned independently over two different reference planes, within a prefixed maximum allowable percentage error from the theoretical discharge. A new technique is adopted to optimize the weir parameters, in order to obtain the maximum ranges of measurement under logarithmic, linear as well as combined characteristics. In the case of linear weir it is shown that it is possible to enhance the linearity range of the chimney weir by more than 540% and for a weir with constant indication accuracy by more than 350%. In addition, about 86% of the overall depth of the designed linear weir and over 90% of the logarithmic weir is converted as the corresponding measurable ranges. Experiments with four typical weirs give consistent constant average coefficient of discharge for each weir confirming the theory. The practical application of the weir in minor irrigation, hydraulic and other engineering fields is highlighted.

Field evaluation of unsaturated hydraulic conductivity models and parameter estimation from retention data

Predictions of two popular closed-form models for unsaturated hydraulic conductivity (K) are compared with in situ measurements made in a sandy loam field soil. Whereas the Van Genuchten model estimates were very close to field measured values, the Brooks-Corey model predictions were higher by about one order of magnitude in the wetter range. Estimation of parameters of the Van Genuchten soil moisture characteristic (SMC) equation, however, involves the use of non-linear regression techniques. The Brooks-Corey SMC equation has the advantage of being amenable to application of linear regression techniques for estimation of its parameters from retention data. A conversion technique, whereby known Brooks-Corey model parameters may be converted into Van Genuchten model parameters, is formulated. The proposed conversion algorithm may be used to obtain the parameters of the preferred Van Genuchten model from in situ retention data, without the use of non-linear regression techniques.

General model of a foam bed reactor

A general model of a foam bed reactor has been developed which rigorously accounts for the extent of gas absorption with chemical reaction occurring in both the storage and foam sections. Its applicability extends to a wide spectrum of reaction velocities. The possibilities of the predominance of the bulk-liquid reaction in the storage section or the absorption with reaction in the foam section can be handled as merely special cases of the general analysis. The importance of foam for carrying out a particular gas-liquid reaction is characterised by a criterion in terms of the fractional rate of reaction in the foam section. Trends of variations in the concentrations of dissolved free A, solute B, and gas-phase A with time of operation of the reactor are presented. The nature of the variation in the fractional rate of reaction in the foam section with time, at different reaction velocities, and the effect of the liquid flow rate (across the storage section) on the transience are also illustrated. Finally, the predictions of the general model have been validated using the available experimental data on the oxidation of sodium sulphide in a foam bed reactor. The agreement between the experimental and the present theoretical information is fairly good, apart from being more insightful than all the previous models of this reactor.