On a Fundamental Formula of a Viscous Fluid

In this paper it was shown that the equation δ∫∫∫Φd×dxdydz=0, which expresses that the dissipation of energy is minimum, is equivalent to Navier-Stokes'equation, if inertia terms are zero and external forces are derived from a potential. Therefore, if fluid flows under the above condition, we can determine the motion by assuming a suitable velocity distribution and deciding its unknown constants so that they satisfy the above equation. By this method, the flow through a straight pipe with isosceles triangle cross-section was solved. The method was also applied to the flow around a sphere, and Stokes'solution was obtained. Each of these examples shows that this energy method is applicable to those problems with success.