Hagen-Poiseuille laminar pipe flow
The speed of water flowing in a pipe is not the same everywhere. Cut the pipe across and measure the speed, and what shape is it? Drag the probe across the section and see. The wall holds on and the middle runs.
Water touching the wall is 0 by no-slip, and it gets faster toward the center, so when you draw the speed as arrows it makes a parabola most bulged at the center. Drag the pushing force and the parabola grows whole, because the viscous friction of the wall holds the edge and only the middle is free to go fast. The edge is held and only the very middle opens a path.
Laminar and turbulent differ from the shape of the distribution. Switch them with a button and laminar is a smooth parabola, while turbulent mixes wildly, the middle goes blunt and flat, and only near the wall it drops sharply, because the lively mixing of turbulence spreads the speed even. Mixing shaves the peak and makes it flat.
A laminar parabola has one clean fact. The maximum speed at the center is exactly twice the average speed over the section, and even when you drag the pushing force this 2 to 1 ratio does not change. So when you compute the flow rate from the average speed, divide the maximum measured at the middle in half. The ratio that the peak is twice the average is fixed.
In symbols, u(r) = umax (1 − (rR)²). It is a parabola, maximum at the center (r=0) and 0 at the wall (r=R), and when you drag the radial position r the speed follows the formula as it is. Toward the edge it falls fast, as a square. The center is the peak and the wall is the floor.
Blood in a vessel flows like this too. The layer stuck to the vessel wall is nearly stopped and the red cells flowing in the middle are the fastest, and when you drag the flow rate the speed of the center cells grows the most. When a vessel narrows the center speed shoots up, and the slow layer near the wall takes part in nutrient exchange and clotting. How much this viscous friction eats the pressure along the pipe is taken up by head loss.