Laminar Approach to Steady Flow in a Circular Tube

Animated plot of approach to steady laminar flow in a circular tube.

Presents an animated plot of the approach of a Newtonian fluid from rest to steady flow in a circular tube based on the analytical solution to the Navier Stokes equation for unsteady fluid flow. The solution involves a infinite sum of Bessel functions which is truncated at five terms. Input includes the flow rate, pipe diameter, and fluid density and viscosity. Output consists of the animated plot of the velocity profile over time until the centerline velocity is within 0.5% of the steady state value. The Reynolds number, flow superficial velocity, time to reach within 0.5% of Vmax, and pressure drop per foot are also calculated.