Why the velocity profile of water is parabolic in shape?
the velocity profile of water is parabolic in shape because of the boundary layer formed when fluid flows either over a plate or through a pipe. the fluid closest to the pipe wall is stationary due to the viscous forces between the fluid on the wall/plate and the wall/plate. The fluid flowing through the middle of the pipe has no effects of viscous forces acting on it as it is far enough away from the wall for viscous forces not to be in effect. the fluid in between has different velocities depending on its distance from the wall. the piece of fluid just next to the centre of the pipe will have a velocity determined by the velocity of the fluid flowing through the centre of the pipe although it will be slightly less as the viscous effects will be more predominant there than at the centre.
