Where U _ p is a characteristic particle velocity, D is the grain diameter ( a characteristic particle size ), and \ nu is the kinematic viscosity, which is given by the dynamic viscosity, \ mu, divided by the fluid density, { \ rho _ f }.
42.
Where \ nu is the kinematic viscosity, \ rho'is the density perturbation that provides buoyancy ( for thermal convection \ rho'= \ alpha \ Delta T ), \ Omega is the rotation rate of the Earth, and \ mathbf { J } is the electric current density.
43.
Here the coordinate system is chosen with x pointing parallel to the plate in the direction of the flow and the y coordinate pointing towards the free stream, u and v are the x and y velocity components, p is the pressure, \ rho is the density and \ nu is the kinematic viscosity.
44.
For common flows ( the ones which can usually be considered as incompressible ar isothermal ), the kinematic viscosity is everywhere uniform over all the flow field and constant in time, so thereis no choice on the viscosity parameter, which becomes naturally the kinematic viscosity of the fluid being considered at the temperature being considered.
45.
For common flows ( the ones which can usually be considered as incompressible ar isothermal ), the kinematic viscosity is everywhere uniform over all the flow field and constant in time, so thereis no choice on the viscosity parameter, which becomes naturally the kinematic viscosity of the fluid being considered at the temperature being considered.
46.
Where \ \ mu _ 0 is the magnetic permeability, \ \ rho is the density of the fluid, \ \ nu is the kinematic viscosity, and \ \ lambda is the magnetic diffusivity . \ B _ 0 and \ d are a characteristic magnetic field and a length scale of the system respectively.
47.
Where " R " is Earth radius, & Omega; is frequency of rotation of the Earth, " g " is gravitational acceleration, & phi; is latitude, & rho; is density of air and & nu; is kinematic viscosity of air ( we can neglect turbulence in free atmosphere ).
48.
Where \ nu > 0 is the kinematic viscosity, \ mathbf { f } ( \ boldsymbol { x }, t ) the external volumetric force, \ nabla is the gradient operator and \ displaystyle \ Delta is the Laplacian operator, which is also denoted by \ nabla \ cdot \ nabla or \ nabla ^ 2.
49.
Further simplification of the momentum equation comes by substituting the volume expansion coefficient, density relationship \ rho _ o-\ rho = \ beta \ rho ( T-T _ o ), found above, and kinematic viscosity relationship, \ nu = \ frac { \ mu } { \ rho }, into the momentum equation.
50.
Since the dimension of kinematic viscosity is length 2 / time, and the dimension of the energy dissipation rate per unit mass is length 2 / time 3, the only combination that has the dimension of time is \ tau _ \ eta = ( \ nu / \ varepsilon ) ^ { 1 / 2 } which is the Kolmorogov time scale.
