<P> In isotropic porous media the off - diagonal elements in the permeability tensor are zero, κ = 0 for i ≠ j and the diagonal elements are identical, κ = κ, and the common form is obtained </P> <Dl> <Dd> q = − κ μ (∇ p − ρ g). (\ displaystyle (\ boldsymbol (q)) = - (\ frac (\ kappa) (\ mu)) \ left ((\ boldsymbol (\ nabla)) p - \ rho (\ boldsymbol (g)) \ right) \, .) </Dd> </Dl> <Dd> q = − κ μ (∇ p − ρ g). (\ displaystyle (\ boldsymbol (q)) = - (\ frac (\ kappa) (\ mu)) \ left ((\ boldsymbol (\ nabla)) p - \ rho (\ boldsymbol (g)) \ right) \, .) </Dd> <P> The above equation is a governing equation for single phase fluid flow in a porous medium . </P>

What are the main assumptions used in darcy's law