Pipe Flow Example
Water flows steadily into the circular pipe with a uniform inlet velocity profile as shown. Due to the presence of viscosity, the velocity immediately adjacent to the inner pipe wall becomes zero and this phenomenon is called the no-slip boundary condition. It is found out that the velocity distribution reaches a parabolic profile at a distance downstream of the entrance and can be represented as
V1(r)=Vmax[1-(r/R)2], where Vmax is the velocity at the center of the pipe and r is the radial distance measured away from the center axis. Use the mass conservation equation, determine Vmax.