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How about this?
Draw a circle of unit radius. The circle depicts the speed and direction of any air particle in the middle of a pipe.
Draw two parallel horizontal lines touching the circle, one on each side. The two straight lines represent a pipe.
From the center of the circle, draw an arrow perpendicular to the top horizontal.
The perpendicular arrow represents the speed of one particle hitting the pipe, contributing some pressure, proportional to the arrow's length.
Now draw a third short horizontal line with a arrow between the other two horizontal lines - representing the speed with which all the air is now moved.
This 'wind' arrow will move any particle moving towards a wall. The vertically moving particle now moves instead at a forward slant. So a particle with the SAME speed as before now has a forward component. The outward component of its speed is reduced for this reason....
This argument cries out for a diagram, in the Newtonian manner!
Brian W