Search results for "analytical solution"
showing 10 items of 31 documents
On thermoeconomics of energy systems at variable load conditions: integrated optimization of plant design and operation
2007
Abstract Thermoeconomics has been assuming a growing role among the disciplines oriented to the analysis of energy systems, its different methodologies allowing solution of problems in the fields of cost accounting, plant design optimisation and diagnostic of malfunctions. However, the thermoeconomic methodologies as such are particularly appropriate to analyse large industrial systems at steady or quasi-steady operation, but they can be hardly applied to small to medium scale units operating in unsteady conditions to cover a variable energy demand. In this paper, the fundamentals of thermoeconomics for systems operated at variable load are discussed, examining the cost formation process an…
Simplified Model to Predict Runoff Generation Time for Well-Drained and Vegetated Soils
2016
The study of generation process of subsurface stormflow, typical of well-drained and high permeable soils, can be theoretically carried out by applying the continuity and the motion equations with the appropriate boundary conditions. However, difficulties and uncertainness on determining soil hydraulic properties and soil physics heterogeneities let this way not always feasible. In a different way, processes dynamic can be derived by the local scale through a coarse graining procedure, allowing to preserve medium motion character, while hydraulic fluctuation of the motion are lost. Following an approach as this, in this paper a simplified model to predict the runoff generation time, the so-…
Discussion of “Unsteady Stage-Discharge Relationships for Sharp-Crested Weirs” by Firouz Ghasemzadeh, Salah Kouchakzadeh, and Gilles Belaud
2021
I would like to thank the authors for writing this interesting article dealing with unsteady stage-discharge relationships for sharp-crested weirs. The operation of triangular and rectangular sharp-crested weirs in unsteady flow conditions was experimentally investigated. Results indicated the presence of looped rating curves, with transposition of the rising and falling limbs compared to that commonly observed in stream gauge ratings. The authors found that the deviation between steady and unsteady flow rates in the looped rating curves depends on the weir type and the hydrograph gradient (i.e., the temporal depth variation), especially when the latter changes rapidly. Finally, they propos…
Hydraulic Design of the Center-Pivot Irrigation System for Gradually Decreasing Sprinkler Spacing
2021
Design strategies that enhance modern irrigation practices, reduce energy consumption, and improve water use efficiency and crop yields are fundamental for sustainability. Although microirrigation is currently a widely applied method, center-pivot irrigation systems have become very popular on large farms, thanks to their automation, wide-coverage, and reliability. Different design procedures have been proposed, even though some aspects have not been solved yet. This paper presents a simple design procedure for center-pivot systems using a gradually decreasing sprinkler spacing along with a pivot lateral, which makes it possible to set favorable and uniformly distributed water application r…
Analytical solution for composite layered beam subjected to uniformly distributed load
2016
ABSTRACTThe article presents an analytical theory for multilayered composite beams subjected to transverse uniformly distributed loads. The formulation is based on a layerwise model characterized by third-order approximation of the axial displacements and fourth-order approximation of the transverse displacements. The layerwise kinematical model is rewritten in terms of generalized variables. The beam equilibrium equations, expressed in terms of stress resultant, allow writing the boundary value governing problem. The layerwise fields are obtained by postprocessing steps. The main advantage is to ensure the accuracy level associated to the layerwise formulations preserving the computational…
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
2010
This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed…
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
2011
Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…
The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media
2012
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…
One pendulum to run them all
2013
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.
Exact Solutions of the Two Dimensional Boussinesq and Dispersive Water Waves Equations
2010
In this paper two-dimensional Boussinesq and dispersive water waves equations are investigated in exact solutions. The Exp-function method is used for seeking exact solutions of the equations through symbolic computation.