From: owner-ammf-digest@smoe.org (alt.music.moxy-fruvous digest) To: ammf-digest@smoe.org Subject: alt.music.moxy-fruvous digest V14 #4936 Reply-To: ammf@fruvous.com Sender: owner-ammf-digest@smoe.org Errors-To: owner-ammf-digest@smoe.org Precedence: bulk alt.music.moxy-fruvous digest Thursday, September 10 2020 Volume 14 : Number 4936 Today's Subjects: ----------------- Prevent the occurrence of Scars Or Marks ["De-pigmentation" Subject: Prevent the occurrence of Scars Or Marks Prevent the occurrence of Scars Or Marks http://covidguide.guru/SO0kV7asxIIjrTjwu0AB5s4ydhbUQPurTOGvmFI8k9s-TJNI http://covidguide.guru/EvyEgzHqgC6ItwgcZlpXApgy9glsRwnrfNauHZq8jzZy1fxU For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate. Newtonian vs non-Newtonian fluids Flow around an airfoil All fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate; it has dimensions {\displaystyle T^{-1}}T^{-1}. Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids. The coefficient of proportionality is called the fluid's viscosity; for Newtonian fluids, it is a fluid property that is independent of the strain rate. Non-Newtonian fluids have a more complicated, non-linear stress-strain behaviour. The sub-discipline of rheology describes the stress-strain behaviours of such fluids, which include emulsions and slurries, some viscoelastic materials such as blood and some polymers, and sticky liquids such as latex, honey and lubricants. Inviscid vs viscous vs Stokes flow The dynamic of fluid parcels is described with the help of Newton's second law. An accelerating parcel of fluid is subject to inertial effects. The Reynolds number is a dimensionless quantity which characterises the magnitude of inertial effects compared to the magnitude of viscous effects. A low Reynolds number (Re<<1) indicates that viscous forces are very strong compared to inertial forces. In such cases, inertial forces are sometimes neglected; this flow regime is called Stokes or creeping flow. In contrast, high Reynolds numbers (Re>>1) indicate that the inertial effects have more effect on the velocity field than the viscous (friction) effects. In high Reynolds number flows, the flow is often modeled as an inviscid flow, an approximation in which viscosity is completely neglected. Eliminating viscosity allows the NavierbStokes equations to be simplified into the Euler equations. The integration of the Euler equations along a streamline in an inviscid flow yields Bernoulli's equation. When, in addition to being inviscid, the flow is irrotational everywhere, Bernoulli's equation can completely describe the flow everywhere. Such flows are called potential flows, because the velocity field may be expressed as the gradient of a potential energy expression. This idea can work fairly well when the Reynolds number is high. However, problems such as those involving solid boundaries may require that the viscosity be included. Viscosity cannot be neglected near solid boundaries because the no-slip condition generates a thin region of large strain rate, the boundary layer, in which viscosity effects dominate and which thus generates vorticity. Therefore, to calculate net forces on bodies (such as wings), viscous flow equations must be used: inviscid flow theory fails to predict drag forces, a limitation known as the d'Alembert's paradox. ------------------------------ End of alt.music.moxy-fruvous digest V14 #4936 **********************************************