By using order of magnitude analysis, the continuity and Navier-Stokes equations can be simplified to the Prandtl
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By using order of magnitude analysis, the continuity and Navier-Stokes equations can be simplified to the Prandtl boundarylayer equations. For steady, incompressible, and two-dimensional flow, neglecting gravity, the result is
\[\begin{aligned} & \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0 \\ & u \frac{\partial u}{\partial x}+v \frac{\partial u}{\partial y}=-\frac{1}{ho} \frac{\partial p}{\partial x}+v \frac{\partial^{2} u}{\partial y^{2}} \end{aligned}\]
Use \(L\) and \(V_{0}\) as characteristic length and velocity, respectively. Nondimensionalize these equations and identify the similarity parameters that result.
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Related Book For
Fox And McDonald's Introduction To Fluid Mechanics
ISBN: 9781118912652
9th Edition
Authors: Philip J. Pritchard, John W. Mitchell
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