The RANS equations along with the time-averaged continuity equation are the main equations to analyze turbulent flow. The classical turbulence theories were proposed by Prandtl and von Kármán. Prandtl simulated the momentum exchange on a macro-scale to explain the mixing phenomenon in a turbulent ...
Cross method. Partially-filled pipe and other open-channel flow solutions are solved with the Manning equation. The format of functions and pressure pipe solutions are designed to be compatible with theiemiscpackage, and the open channel hydraulics solutions are modifications of code in that package...
* Know the conditions required in order to use a simpler equation instead of the Kindsvater-Carter equation to calculate the flow rate over a suppressed rectangular weir and over a contracted rectangular weir for given head over the weir and weir dimensionsHarlan H. Bengtson...
This chapter explains how to solve steady-state gradually varied open channel flow problems. The gradually varied flow (GVF) equation is obtained by differentiating an expression for total head with respect to distance. The concept of sub-critical and supercritical flow are discussed in the context...
Fixes #252, incorrect math computing half digits (Kimball Thurston 2019-07-22) Based on float / double math for base 10 digits, with 1 bit of rounding error, the equation should be floor( mantissa_digits - 1 ) * log10(2) ), which in the case of half becomes floor( 10 * log10(...
Simulations performed using the Nernst-Planck mass equation indicated that [K+] near the membrane surface fell markedly below the average [K+] of the bulk extracellular solution during K+ influx, and, notably, that fluid flow restored the decreased [K+] at the cell surface in a flow rate-...
For example, in OpenFOAM, there are mesh motion ‘engines’ (displacement maps), which define M as an interpolation or a solution of a Laplace equation for \({\textbf{d}}\) with variable diffusivity, i.e. the Laplacian mesh motion, given boundary displacements \({\textbf{d}}|_{\partia...
Within the vegetated layer, an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted. In the non-vegetated layer, a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated. Based on the studied ...
The pressure toolbox uses Poisson formulation of the flow equation to estimate the pressure field, assuming the boundary conditions of the field is known; using an iterative technique [2]. The POD toolbox was developed to extract energetic modes from velocity or vorticity fields to study coherent...
3 & Jeffrey Comer4 Within the solubility–diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous ...