Streamwise Pressure Gradient on Curved Walls

Could someone help me to understand how can a wall generate differents streamwise pressure gradients just by its curvature? I can understand how it works in cross-flow (perpendicular to the streamline) but i don't have the intuition neither the math approach to the streamwise direction.

• Do you mean a flat wall/plate or a curved one like the one in the picture? You don't understand the "decreasing" and "increasing pressure" part of the story, correct? But you do understand the variation in y, right? Feb 9, 2023 at 19:10
• A curved one. Correct, i can't relate how there is variation in the pressure gradient streamwise oriented due to curvature, what leads to acceleration / deccelaration and separation. Yes, if i understood right it happens in y due to the resultant centrifugal force, so pressure "outside" a curved streamline is higher than the pressure applied from the "inner side". Feb 9, 2023 at 19:30
• Regarding the pressure and velocity variation along x I'd suggest you to read this very good answer, especially the part "Flow over the upper side of the wing". Regarding the variation in y, this is going to help. And no, it has nothing to do with centrifugal forces ðŸ˜‰ Feb 9, 2023 at 20:00
• About 'y' direction: i wasnt talking about velocity gradient in the normal direction and close to the wall, but how a pressure field vary in the normal direction when the streamline is curved, like in this paper: /www3.eng.cam.ac.uk/outreach/Project-resources/Wind-turbine/… With this we can realize how the normal gradient of pressure is given for a flow over an curved shape. Feb 9, 2023 at 23:19
• 'x' direction: I don't know if i understood it right but, to maintain the flow aligned with the curved shape, the pressure acting on the flow direction must adjust the velocity to not create 'vacuums'? Feb 9, 2023 at 23:26