scholarly journals Lateral structure of uniform flow

2004 ◽  
Vol 6 (2) ◽  
pp. 101-108
Author(s):  
Rodney J. Sobey

The concept of uniform flow is traditionally associated with a cross-section-integrated description of channel flow. In some analyses of flow in wide channels, it may be appropriate to adopt a depth-integrated description. The ensuing lateral structure of the depth-integrated flow is investigated at uniform flow. The steady state ordinary differential equation for the lateral structure is established, along with the formulation as a boundary value problem. An integral part of the formulation is the relationship between the channel resistance models for cross-section-integrated and depth-integrated descriptions, respectively. Predictions are shown for a rectangular channel and for an irregular channel.

Author(s):  
Bohua Sun

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, a complex-form ordinary differential equation (ODE) for the small symmetrical deformation of an elastic torus is successfully transformed into the well-known Heun's ODE, whose exact solution is obtained in terms of Heun's functions. To overcome the computational difficulties of the complex-form ODE in dealing with boundary conditions, a real-form ODE system is proposed. A general code of numerical solution of the real-form ODE is written by using Maple. Some numerical studies are carried out and verified by both finite element analysis and H. Reissner's formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell.


1962 ◽  
Vol 2 (4) ◽  
pp. 425-439 ◽  
Author(s):  
A. Erdéyi

In this paper we shall discuss the boundary value problem consisting of the nonlinear ordinary differential equation of the second order, and the boundary conditions.


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