![]() ![]() G = Acceleration due to gravity (considering earth g = 9.8 m/s) P fluid = Pressure at a point taken in fluid The following relation can be used to calculate the pressure in fluids. Gravity, acceleration, or forces outside a closed container are the factors that cause this pressure. Depending on the context of use there are several in which pressure can be expressed.įluid pressure can be defined as the measurement of the force per unit area on a given object on the surface of a closed container or in the fluid. Pressure is an important physical quantity-it plays an essential role in topics ranging from thermodynamics to solid and fluid mechanics. When stress is interpreted as linear momentum flux the kinematic viscosity appears as the key propertyīy doing this transformation, the gradient is transformed from the velocity gradient to the linear momentum concentration gradient, and the kinematic viscosity can be correctly interpreted as the linear momentum diffusivity.The pressure is a scalar quantity that is defined as force per unit area where the force acts in a direction perpendicular to the surface. Going ahead with this approach, the Newton’s Law of viscosity can be slightly transformed for constant density, by multiplying and dividing the right side by density, ρ, and then appears the kinematic viscosity, ν, instead of the dynamic viscosity, μ: The Transport Phenomena approach includes a minus sign in the Newton’s Law of viscosity because of the fact that stress is interpreted as linear momentum flux Therefore, it is necessary to include a minus sign in the Newton’s Law of Viscosity: τ versus γ The Transport Phenomena approach interprets the stress applied as a manifestation of the linear momentum transfer between the regions of fluid moving faster and regions of fluid moving slower.Īccording to this interpretation, the shear stress is the linear momentum flux (linear momentum flow per unit area):Īs long as the linear momentum is transported from higher velocities to lower velocities, it always is transported in the opposite direction of the velocity gradient. ![]() the resulting force (direction x, F x) is the product of the applied stress ( τ xy) and the acting area: ( A xz, oriented according to the y-direction) 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 ![]()
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