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The sound of an organ pipe is made up of a set of harmonics formed by acoustic resonance, with wavelengths that are fractions of the length of the pipe.There are nodes of stationary air, and antinodes of moving air, two of which will be the two ends of an open-ended organ-pipe (the mouth, and the open end at the top). [1]
Averaging the equations gives the Reynolds-averaged Navier–Stokes (RANS) equations, which govern the mean flow. However, the nonlinearity of the Navier–Stokes equations means that the velocity fluctuations still appear in the RANS equations, in the nonlinear term − ρ v i ′ v j ′ ¯ {\displaystyle -\rho {\overline {v_{i}^{\prime }v_{j ...
Accidental release source terms are the mathematical equations that quantify the flow rate at which accidental releases of liquid or gaseous pollutants into the ambient environment which can occur at industrial facilities such as petroleum refineries, petrochemical plants, natural gas processing plants, oil and gas transportation pipelines, chemical plants, and many other industrial activities.
Examples of governing equations include: Manning's equation is an algebraic equation that predicts stream velocity as a function of channel roughness, the hydraulic radius, and the channel slope: v = k n R 2 / 3 S 1 / 2 {\displaystyle v={k \over n}R^{2/3}S^{1/2}}
The exact k-ε equations contain many unknown and unmeasurable terms. For a much more practical approach, the standard k-ε turbulence model (Launder and Spalding, 1974 [3]) is used which is based on our best understanding of the relevant processes, thus minimizing unknowns and presenting a set of equations which can be applied to a large number of turbulent applications.
Equation-free modeling is a method for multiscale computation and computer-aided analysis.It is designed for a class of complicated systems in which one observes evolution at a macroscopic, coarse scale of interest, while accurate models are only given at a finely detailed, microscopic, level of description.
The Taylor microscale is the intermediate length scale at which fluid viscosity significantly affects the dynamics of turbulent eddies in the flow. This length scale is traditionally applied to turbulent flow which can be characterized by a Kolmogorov spectrum of velocity fluctuations. In such a flow, length scales which are larger than the ...
In mathematics and physics, multiple-scale analysis (also called the method of multiple scales) comprises techniques used to construct uniformly valid approximations to the solutions of perturbation problems, both for small as well as large values of the independent variables. This is done by introducing fast-scale and slow-scale variables for ...