Determination of the curvature of the magnetic fluid under the external forces

In this paper, the method to obtain the shape of the magnetic fluid under the external force is derived. For the shape analysis of the magnetic fluid, Maxwell equation for the magnetic-field energy and Navier-Stoke equation for the mechanical energy of the fluid need to be solved simultaneously. The main idea of the method is that dynamic constant is the same value on the fluid surface because of the boundary equilibrium conditions. The final curvature of the fluid is determined under constraint of the magnetic-fluid volume. The effects of the gravitational force, centrifugal force, and external pressure on the shape of the magnetic fluid are analyzed and the computed results agreed well with photographic images.