Originally Posted by ShoeDLG
The Bernoulli equation lets you relate the net change in pressure between two points on a streamline to the net change in flow velocity between those points. Again, the equation is derived by integrating all of the infinitesimal pressure changes along the path between the two points… there’s no getting around that..
Getting back to algebra and useing the cylinder for well documented simplicity.
Fluid texts all show the source/sink pattern and the simple formula for flow velocity relative to the surface. (ideal etc.) I reconsile this with the cylinder V and find the actual instantainious velocity relative to the remote still air. ( v is virtually never at right angles to v')
At every location between the stagnation areas the velocity of the flow next to the surface is one V in its source/sink direction. In the direction of its path there is no acceleration and no change in speed. The -V we see at the top of the cylinder indicates direction only and not a difference in speed.
All pressure change must then come from normal accelerations. The primary acceleration for the cylinder is normal to the true flowpath. Lift is determined by acceleration normal to the surface which is a component of that primary acceleration.