Search results for "analytical solution"

Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments

2020

In the field of hydrology, stage&ndash

Linking the Kinetic Energy Fraction and Equivalent Length Method for Trickle Irrigation Design under Local Losses

2020

New methods using analytical relationships to design drip irrigation laterals and subunits have been introduced in recent years based on the assumption that minor losses can be neglected. This assumption could be relaxed by applying the equivalent method, which makes it possible to account for minor losses, such as those caused by emitter connections, through formulas based on the rationale that an equivalent length of the drip lateral produces the same losses. However, equivalent length formulas are empirical; thus, they do not necessarily cover the entire range of conditions in the real-world contexts in which the formulas will be applied, and their extrapolation could lead to erroneous r…

Analytical approach extending the Granier method to radial sap flow patterns

2020

Abstract The Granier thermal dissipation (TD) method is probably the most applied method to compute the transpiration flux of trees, due to its simplicity and effective compromise between theory and data availability. Starting from the heat transfer equations at the basis of Granier’s method, the objective of this paper is to derive an analytical solution for the transpiration flux to extend the sap flow equations to the radial domain. We adopted a flexible approach to cope with the differences in radial sapflow density (SFD) profile shapes that are known to occur in relation to wood anatomy (diffuse porous vs. ring- or non-porous xylem). With this purpose, we investigated the robustness of…

An improved numerical solver of the 2D diffusive shallow waters equations over unstructured triangular meshes

2009

On the instability of an axially moving elastic plate

2010

Problems of stability of an axially moving elastic band travelling at constant velocity between two supports and experiencing small transverse vibrations are considered in a 2D formulation. The model of a thin elastic plate subjected to bending and tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of an analytical approach. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence (buckling). Then the static forms of instability are investigated, and critical regimes are studied as functions of geometric and mechanical problem param…

A beam theory for layered composites subjected to uniformly distributed load

2015

A theory for multilayered composite beams undergoing transverse uniformly distributed loads is presented. The formulation starts by assuming a layer-wise kinematical model characterized by third order approximation of the axial displacements and fourth order approximation of the transverse displacements. By enforcing the point-wise balance equations as well as the interface continuity conditions, the layer-wise kinematical model is rewritten in terms of a set of generalized kinematical variables associated with the beam as a whole. Stress resultants are then obtained in terms of the generalized variables derivatives and of the normal stresses applied to the top and bottom surfaces of the la…

Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains

2016

We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…

Centre-pivot irrigation system design for uniform water application rate

2020

<p>In the last few decades, the use of centre-pivot irrigation systems has significantly increased, since it makes farming easier, is more efficient and less time-consuming compared to the other irrigation systems. Several studies have been focused on the hydraulics of the centre-pivot systems. Standard high-pressure impact sprinklers or low-pressure spray sprinklers or Low Energy Precision Application (LEPA) systems are generally mounted on the pipeline.</p><p>To ensure the uniformity of water application, the centre-pivot design requires increasing the flow rates along the lateral, because the sprinklers farther from the pivot move faster, and th…

Onset of convection in a porous rectangular channel with external heat transfer to upper and lower fluid environments

2012

Published version of an article in the journal: Transport in Porous Media. Also available from the publisher at: http://dx.doi.org/10.1007/s11242-012-0018-9 The conditions for the onset of convection in a horizontal rectangular channel filled with a fluid saturated porous medium are studied. The vertical sidewalls are assumed to be impermeable and adiabatic. The horizontal upper and lower boundary walls are considered as impermeable and subject to external heat transfer, modelled through a third-kind boundary condition on the temperature field. The external fluid environments above and below the channel, kept at different temperatures, provide the heating-from-below mechanism which may lead…

Closed-form solutions of the energy balance equation for drip laterals under the Darcy-Weisbach resistance formula

2018

Many studies have investigated easy methods to design drip laterals, as well as the best resistance equation to use, which is fundamental to accurately account for friction losses. This paper addresses both the features of lateral design relationships and the influence of the friction-loss equation on the design variables. First, simple closed-form solutions of the energy balance equation for both sloped and horizontal drip laterals are derived with the simplified Darcy-Weisbach resistance formula by assuming the Darcy friction factor as invariant versus the Reynolds number. Second, an error analysis is performed assuming the friction factor as constant in the design, which is compared to u…