Viscosity Loss of energy due to internal friction between molecules moving at different velocities. Higher resistance to flow Watch viscous honey clip.Viscosity What characterizes a viscous liquid? Helmholtz-Hodge Decomposition Input Velocity field Curl-Free (irrotational) Divergence-Free (incompressible) + =Īside: Pressure as Lagrange Multiplier Interpret as an optimization: Find the closest to where A Lagrange multiplier to enforce the constraint is exactly pressure. Pressure is the force required to ensure that.Incompressibility By divergence theorem: But this is true for any region, so everywhere. Integrate the flow across the boundary of a closed region: Incompressibility Intuitively, net flow into/out of a given region is zero (no sinks/sources). Incompressibility Compressible velocity field Incompressible velocity field Exceptions: high velocity, high pressure, ….In Navier-Stokes we saw: Velocity is advectedby itself!Īdvection i.e., The scalar components of the vector are each advected in the same way. Operator splitting Break the equation into steps: Īdvection Previously, we considered advection of a passive scalar quantity,, by velocity. In full… Change in velocity at a fixed point Advection Forces (pressure, viscosity gravity,…) Possibilities for more exotic fluid types:.What are the forces on a fluid? Primarily for now: Navier-Stokes Density Acceleration = Sum of Forces Expanding the material derivative… Specialized for fluids: “Navier-Stokes Equations”. For general materials, we have Newton’s second law: F = ma.Think of colored dye or massless particles drifting around in fluid. Change at the current (fixed) point.Īdvection To track a quantity T simply moving (passively) through a velocity field: This is the advection equation. Change at a point moving with the velocity field. Material Derivative This is called the material derivative, and denoted. Time derivatives Mathematically: Chain rule! Definition of Choose Following the path, the point moves to a cooler/warmer location.Heating/cooling occurs at the current point.Relating Eulerian and Lagrangian Consider the temperature at a point following a given path. Eulerian: A fixed grid of temperature values, that temperature flows through.Lagrangian: Set of movingparticles, each with a temperature value.Lagrangian Consider an evolving temperature field. weather station on the ground (Eulerian)Įulerian vs. Eulerian: Point of reference is stationary. Lagrangian Lagrangian: Point of reference moves with the material. Internal forces depend on velocities, not displacements Watch fluid simulation clipsĮulerian vs.Use the picture tools menu bar to change pictures or apply different effects.Fluid Animation Christopher Batty November 17, 2011 These slides present a scenery image behind image masks that are easily replaceable. You can customize liquid image masks and semi-transparent fluid shapes with PowerPoint formatting features. The animated slides are designed to feature conclusions, summaries, or completion of work in a clear and simple layout.Īnimated Template of images marks for PowerPoint are advanced shapes with an artistic design. Animated templates of image masks present rotation of fluid shapes with the fixed image in the background. In project meetings, fluid image mask slides can describe work completion or next plan for work using minimal slide design. agenda for proving the presentation summary. You can add animated liquid mask template at the start, i.e. The Animated Liquide Images Mask for PowerPoint is used in various levels of business presentations. These graphic slides are helpful in concluding a topic with images to support textual content. You can present ideas such as of annual report, new year plan, company’s vision using fluid shapes. The fluid shapes in animated liquid images are suitable for summarizing a bigger picture of the topic. Generally, image masks are used in business slide decks for an artistic touch to a professional presentation. It gives an idea of displaying images from a creatively cropped background. Masking allows random fluid shapes over high-quality images to create adjustable layers of certain portions. With sceneries in the background and geometric patterns on solid areas on slides, the liquid images present masking techniques. The Animated Liquid Images Mask for PowerPoint presents cutout image designs over a background image.
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