In the present work, we analyze theoretically the flow of magnetic fluids in a circular pipe with longitudinal magnetic field. We used governing equations induced Shliomis and Polar theory of Eringen. Using theoretical equations and distributions for the velocity, vorticity and angular velocity as the magnetic response, it is shown that magnetic fluid flow is non-Newtonian fluid. We investigate dynamic characteristic of magnetic fluid by comparing longitudinal magnetic field with transverse magnetic field. And, the limits, influence magnetic fluid, of the intensity of the magnetic field with polar, size and magnetic effect parameters are shown.