As a first step toward understanding how much blood flows through the
arteriole, we will examine how fast the blood
(or other fluid) is moving at each point within the vessel. Because the flow is
laminar, we can treat the fluid as though made up of thin cylindrical sheets.
Using Newton's second law of motion (F=ma) and the precise definition of
viscosity, one can use the theory of calculus to find the law that governs
the speed of the fluid at each point in the tube.
More specifically, we measure
the distance of the point from the center of the tube to be at a specific
radius (r), at which point the speed is given by the formula
The graph of this formula is easily found to be a parabola.
Let us make a few initial observations. First, notice that the blood is not
moving when r=a. This means that no slipping is allowed between the blood
and the vessel's wall. Secondly, notice that the vertex occurs when
r=0. The fastest blood is at the center of the arteriole.
More About Velocity
You can explore the following pages to understand better the velocity and its
relationship to the flow: