Acceleration of fluid 'material' is written as \frac{D \underline{\mathbf{u}}}{D t}=\frac{\partial \underline{\mathbf{u}}}{\partial t}+\underline{\mathbf{u}} \cdot \nabla \underline{\mathbf{u}} in terms of an Eulerian vector field u(x, t). Consider now steady flow through converging section of pipe (in some flow loop for example). The first term is zero whereas the second is not due to spatial gradients in the flow field. Imagine now putting that flow loop on a train moving with a steady velocity U. Does the acceleration of the fluid in the pipe change? Show why or why not mathematically. /3

Solved: Acceleration of fluid 'material' is written as \frac{D \underline{\ma

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Acceleration of fluid 'material' is written as \frac{D \underline{\mathbf{u}}}{D t}=\frac{\partial \underline{\mathbf{u}}}{\partial t}+\underline{\mathbf{u}} \cdot \nabla \underline{\mathbf{u}} in terms of an Eulerian vector field u(x, t). Consider now steady flow through converging section of pipe (in some flow loop