This simulation demonstrates the velocity profile for laminar flow. At the start of the simulation each chunk of fluid, or each molecule, is at the same x location. As the fluid flows the molecules near the center of the pipe flow fastest, and the molecules next to the wall have the slowest velocity. Note that the molecules only have non-zero velocities in the x direction; i.e., the fluid does not move in the r direction.
The velocity profile in the case of laminar flow can be solved
analytically. Let 
be the velocity of the fluid in the x direction at a radial position r in the pipe, given by
where R is the radius of the pipe, i.e., r = R is at the pipe wall. The displacement of the fluid is given by
Hence, the molecules (or fluid) in the center of the pipe keep getting farther and farther ahead of the molecules (or fluid) near the center of the pipe.
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