If the fluid is isotropic as well as Newtonian, the viscosity tensor will have only three independent real parameters : a bulk viscosity coefficient, that defines the resistance of the medium to gradual uniform compression; a dynamic viscosity coefficient that expresses its resistance to gradual shearing, and a rotational viscosity coefficient which results from a coupling between the fluid flow and the rotation of the individual particles.
42.
\delta = the thickness of the boundary layer : the region of flow where the velocity is less than 99 % of the far field velocity v _ \ infty; x is position along the semi-infinite plate, and Re is the Reynolds Number given by \ rho v _ \ infty x / \ mu ( \ rho = density and \ mu = dynamic viscosity ).
43.
Where \ mu is the dynamic viscosity, a is the particle radius, \ mathbf { v } ^ { \ infty } is the ambient flow, \ mathbf { U } is the speed of the particle, \ mathbf { \ Omega } ^ { \ infty } is the angular velocity of the background flow, and \ mathbf { \ omega } is the angular velocity of the particle.
44.
The total discharge, Q ( having units of volume per time, e . g ., ft?/ s or m?/ s ), is proportional to the intrinsic permeability, K, the cross sectional area, A, and rate of pore pressure change with distance, \ frac { u _ b-u _ a } { L }, and inversely proportional to the dynamic viscosity of the fluid, \ mu.
45.
In these equations " r H " presents the hydrodynamic radius of the colloids, \ nu the speed of electrophoretic migration, \ eta the dynamic viscosity of the solutions, \ varepsilon _ { 0 } dielectric constant in vacuum, \ varepsilon _ { r } is water s relative dielectric constant at 298 K, \ zeta is the zeta potential, " E " is the electric field.
46.
For example, if the mass of the vehicle is 1000 kg, A = 0.1 m ^ 2, h = 0.1mm, and v = 10 m / s and dynamic viscosity of water is 1.002 * 10 ^-3 N * s / m ^ 2 and water density 0.9982 g / cm ^ 3, I get a stopping distance of 206m, assuming the water plane thickness h and wetting area A do not change.
47.
Under the action of gravity, a particle acquires a downward speed of " v " = ? " mg ", where " m " is the mass of the particle, " g " is the acceleration due to gravity, and ? is the particle's George Stokes had shown that the mobility for a spherical particle with radius " r " is \ mu = \ tfrac { 1 } { 6 \ pi \ eta r }, where ? is the dynamic viscosity of the fluid.
