Let us suppose that a fluid is flowing through a pipe (fully filled) of uniform cross section. The fluid is ideal and hence must flow in a streamlined path and must be in a steady state. This means that the path of particles of fluid must never intersect (streamlined flow) and hence the velocity of all particles must be parallel to the walls of the pipe and equal at point (steady flow).
Note: The figure below is a horizontal cross section of the pipe
Since the path is streamlined, the velocity of particles are parallel to each other and to the wall, therefore the particle A will also have velocity parallel to the walls and hence no component of velocity of A is towards the wall.
- So how will A exert any pressure on the wall since there is no component of velocity in the direction of wall (it will not strike the wall and hence not exert pressure on it.)
Moreover since the velocities of particle A and particle B are parallel (both particles are in the same horizontal plane), they will not exert pressure on each other? Is it wrong.
What am I getting wrong about streamlined flow?
- If the pressure is due to the vibration of a particle which will result in collision with the wall, then my further question is that according to Bernoulli equation, the pressure is different at different velocity but since the the pressure is caused by the vibration of fluid particle and not due to its velocity perpendicular component (which is a contradiction to my reasoning above that perpendicular component of velocity will be zero) then why will the pressure change at all when it is flowing with different velocity (due to increase/decrease in cross sectional area)?
Edit: I got this question because I was watching a video on Bernoulli Equation on an molecular scale.(https://youtu.be/TcMgkU3pFBY) Here, they explain how there is low pressure in smaller cross-sectional (and higher velocity) area due to less perpendicular velocity and hence collisions with the wall are less. But in the case of an ideal fluid the flow should be streamlined hence there should not be any perpendicular velocity(?), which leaves the explanation in the video incomplete for ideal fluids. Am I messing up pressure on the wall with the pressure inside the fluid. If not and considering there will be no perpendicular component , then how will we explain the pressure change on walls due to Bernoulli Principle.
Because if the inter-molecular repulsion at X is some quantity, then the inter-molecular repulsion at Y must be less that quantity(as pressure is less due to Bernoulli Principle at Y), which seems contradictory to me.