Instead of the control-volume formulation, such as the Reynoldstransport theorem (Eqs. 11.5 and 11.6 of WMD), please consult fluidmechanics textbooks such as “Viscous Fluid Flow†by F.M. White(Chapter 1 & 2) and derive the Navior-Stokes equation for aNewtonian fluid flow starting from Newton’s second law: F= mawhere F, m, a are the force, mass,and acceleration respectively, following a fluid element.In the derivation you should state (or argue) clearly theassumptions you made and the following key terms:
(1) How the stress and strain rate tensors are defined on afluid element and their relationship.
(2) the definition of a “Newtonian†fluid,
(3) the definition of the coefficient of viscosity and thecoefficient of bulk
viscosity (the second coefficient of viscosity)
(4) the relation between the thermodynamic pressure and the meanflow
pressure
