Flow through circular curved stationary pipe

R.Sripriya

I am studying flow through stationary circular(round) pipe.The fluid enters the pipe with a constant velocity. Upon entry, the two surfaces of the pipe experience a pressure difference, the inner surface that of p and the outer surface P+dp. Due to this pressure gradient and the tendency of the liquid to flow from a region of high pressure to low pressure the fluid flows from the outer rim to the inner rim. At steady state one can observe that closer to the inner rim we have liquid of high velocity and at the outer rim low velocity. How is this kind of flow sustained throughout the pipe. a velocity contour plot does not show any back mixing or secondary flows anywhere. can anyone explain this phenomenon