Navier Stokes

Figure 2.3.5): a resistive force R , a buoyant force B , and its weight w due to gravity. The buoyant force is equal to the weight of the fluid displaced by the object. For a slowly moving spherical body of radius a , the resistive force is given by Stokes’3 law R = 6π µa |v |, where v is the velocity of the body, and µ is the coefficient of viscosity of the surrounding fluid. R B a w FIGURE 2.3.5 A body falling in a dense fluid. (a) Find the limiting velocity of a solid…

investigate water flow in the unsaturated zone or if flow is turbulent. To further investigate these shortcomings of Darcy’s Law, attempts have been made to derive a similar equation for fluid flow through porous media from physical laws, such as the Navier–Stokes equation (see Gray and Miller 2004). Although many groundwater scientists are well versed in applied mathematics, most are more interested in expressions that consist of parameters than can be readily measured—a nod to Darcy’s…