The classical Fluid Mechanics approach interprets the stresses in a fluid in the same fashion as the Solids Mechanics, i.e.Transport PhenomenaĪn important difference can be found on the way the Newton’s Law of Viscosity is written depending on the chosen approach: Non-Newtonian Fluids are those fluids for which the apparent viscosity changes according with the applied shear rateįor a Newtonian fluid, the apparent viscosity is independent on shear rate but still depends on pressure and temperature Fluid mechanics vs.In other words, the ratio shear stress to shear rate is independent on the shear rate (or shear stress) and depends only on the nature of the fluid (chemical composition) and the prevailing temperature and pressure. Newtonian Fluids, those for which the relationship between shear stress and shear rate (velocity gradient) is independent on the applied shear.Philisophiae Naturalis Principia Mathematica, Isaac Newton (1686) The Newton’s Law of Viscosity serves as the classification criterion for grouping the fluid into two blocks, according to the behavior of the apparent viscosity: The apparent viscosity dependence on shear rate defines if a fluid behaves as Newtonian or Non-NewtonianĪccording to Macosko (1994) in his book “Rheology: Principles, measurements and applications”, “…a lthough Newton in 1686 had the right physical insight, it was not until 1845 that Stokes finally was able to write out this concept in three dimensional mathematical form …and… only in 1856 were Poiseuille’s capillary flow data analyzed to prove Newton’s relation experimentally”. The velocity gradient is known in fluid mechanics as the shear rate: The fluid model developed by Newton is an “ideal” fluid that behaves in such a way that when applied a shear stress, τ xy, the developed velocity gradient, dv x/dy, is proportional to the stress. Jose Angel Sorrentino General formulation
The SI unit for flow rate is =Av, where A is the cross-sectional area of the pipe and v is the magnitude of the velocity.Editor: Prof. Here, the shaded cylinder of fluid flows past point P in a uniform pipe in time t. This can occur when the speed of the fluid reaches a certain critical speed.įigure 14.26 Flow rate is the volume of fluid flowing past a point through the area A per unit time. In turbulent flow, the paths of the fluid flow are irregular as different parts of the fluid mix together or form small circular regions that resemble whirlpools. The second diagram represents turbulent flow, in which streamlines are irregular and change over time. This is a special case of laminar flow, where the friction between the pipe and the fluid is high, known as no slip boundary conditions. Note that in the example shown in part (a), the velocity of the fluid is greatest in the center and decreases near the walls of the pipe due to the viscosity of the fluid and friction between the pipe walls and the fluid. The first fluid exhibits a laminar flow (sometimes described as a steady flow), represented by smooth, parallel streamlines. The diagrams in Figure use streamlines to illustrate two examples of fluids moving through a pipe. The velocity is always tangential to the streamline. A streamline represents the path of a small volume of fluid as it flows. The colors represent the relative vorticity, a measure of turning or spinning of the air.Īnother method for representing fluid motion is a streamline. Notice the circulation of the wind around the eye of the hurricane.
Figure 14.24 The velocity vectors show the flow of wind in Hurricane Arthur.
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