## Flow over flat surface

There is an inviscid incompressible steady flow over a flat surface. The upper part of the flow has a higher static pressure than the lower part. Neglecting body forces, the momentum equation for a control volume in the part of the flow with lower static pressure reduces to

$$\displaystyle\rho\iint_S (V\bullet dS)V=-\iint_S pdS$$

Does this mean that there is a net influx of momentum into the control volume from the upper part of the flow?

How does this translate physically in terms of molecules? If the assumption that the flow is steady is dropped, will the momentum of the flow increase? Will this have any effect on the pressure of the flow
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