Show how the differential form of the (mathrm{x})-component momentum equation [Equation (2.70a)] can be expressed using the

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Show how the differential form of the \(\mathrm{x}\)-component momentum equation [Equation (2.70a)] can be expressed using the substantial derivative:

\[ \frac{\partial(ho u)}{\partial t}+abla \circ(ho u \boldsymbol{V})=-\frac{\partial p}{\partial x}+ho f_{x}+\left(F_{x}\right)_{v i s c o u s} \]

Next, show how your result above can be generalized for the full momentum conservation equation (in differential form):

\[ \frac{\partial(ho \boldsymbol{V})}{\partial t}+abla \circ(ho \boldsymbol{V} \boldsymbol{V})=-abla p+ho \boldsymbol{f}+\boldsymbol{F}_{\text {viscous }} \]

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Fundamentals Of Aerodynamics ISE

ISBN: 9781266076442

7th Edition

Authors: John D. Anderson, Jr, Christopher P Cadou

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