Question 10.14.6: For an incompressible viscous fluid moving under a conservat...
For an incompressible viscous fluid moving under a conservative body force, prove the following:
\begin{matrix}(i)&\triangledown^2\left(\frac{p}{\rho}+\chi+\frac{1}{2}v^2\right)=div(\textbf{v}\times\textbf{w})&(10.14.41)\\(ii)&\triangledown^2\left(\frac{p}{\rho}+\chi\right)=\frac{1}{2}\textbf{w}^2-\textbf{D.D}&(10.14.42)\end{matrix}
Further, if the motion is irrotational, deduce that
\begin{matrix}(iii)&\triangledown^2v^2=2\textbf{D.D}\geq 0&(10.14.43)\end{matrix}
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