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Newtonian fluids: where stress is directly proportional to rate of strain; Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives. Newtonian fluids follow Newton's law of viscosity and may be called viscous fluids. Fluids may be classified by their compressibility:
For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid. In this case, the material derivative then describes the temperature change of a certain fluid parcel with time, as it flows along its pathline (trajectory).
This "special" derivative is in fact the ordinary derivative of a function of many variables along a path following the fluid motion; it may be derived through application of the chain rule in which all independent variables are checked for change along the path (which is to say, the total derivative).
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.
Assuming conservation of mass, with the known properties of divergence and gradient we can use the mass continuity equation, which represents the mass per unit volume of a homogenous fluid with respect to space and time (i.e., material derivative) of any finite volume (V) to represent the change of velocity in fluid media ...
A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are ... is the partial derivative in the direction x of the flow velocity ...
Fluid kinematics is a term from fluid mechanics, [1] ... The time derivative portion is denoted as the local derivative, and represents the effects of unsteady flow ...
Thus for an incompressible inviscid fluid the specific internal energy is constant along the flow lines, also in a time-dependent flow. The pressure in an incompressible flow acts like a Lagrange multiplier , being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no ...