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Physics 2065A/B
Bob Sica

LIFT Airfoils -More streamlined shapes have less drag (See Slide 3 for airfoil images) Drag on a Sphere No Turbulence -Recall for Laminar flow (no turbulence) the streamlines around a sphere would be irrotational and symmetric -The front of a sphere would feel high pressure drag force due to the wind but… -This drag force would be equal and opposite to the high pressure thrust (negative drag) behind the sphere (similar to the force of gravity vs. the normal force) -Net result: a sphere feels no drag force - Turbulence -However, when the Reynolds number is large enough, vortices begin to form -The vortices stay attached until Re becomes large and then detaches from the sphere and break down to turbulence (View photos) -Vortices have all types of different sizes and different flows and appear at different lengths behind the ball -Breakdown of the vortices= turbulence Energy has to break down to smaller and smallers scales, acting as a drag force and slowing it down -The vortices (and later turbulence) greatly decrease thrust on the ball=net drag Richardson’s Rhyme: “Big whorls have little whorls that feed on their velocity, and little whorls have lesser whorls and so on to viscosity”  Large vortic structures breakdown to smaller and smaller vortec structures, eventually into individual molecules which create viscosity Flow Separation -Drag on a sphere is caused by flow separation over its rear face The less the flow separartes, the less the drag -Minimizing flow separation decreases drag and keeps the flow laminar E.g The Golf Ball -Why covered with dimples? To make it go farther -The pressure difference which causes the drag on a ball occurs in a thin region near the ball called the Boundary layer Dimples -A smooth sphere has a laminar boundary layer that separates and causes a large wake behind the sphere causes friction and the air sticks to the ball longer -A dimpled sphere has a turbulent boundary layer that speeds up flow around the sphere and decreases the wake Increases the boundary layer, decreasing the friction on the ball and keeping the flow around the ball longer -Less energy into resisting turbulence and more into moving forward -CFD example (computational flow dynamics), allows numeric examination rather than just trial and error Reynolds Number for Spheres -Chart represents drag coefficient vs Reynolds number -A smooth spehere has a large drag coefficient until Re>100000 -Re<200000: the dimpled sphere has less drag (all reasonable speeds for a golf ball) Vortex Generators (on the tip of the wings of Airplanes) -Why don’t wings have dimples like a golf ball? -The drag on blunt objects is different from streamlined shapesVortex generators can increase lift on a wing by causing turbulence -Pressure changes in the boundary layer (air drag) are much smaller than skin drag Skin Friction Drag -The decrease in pressure is gradual around an airfoil compared to a sphere -Skin friction drag dominates -Caused by air molecules dragging on the wing’s surface -Skin friction is an interaction between a solid and a gas, so it depends on both the wing material and air viscosity Lift -The upward force that keeps and airplane flying is called lift -Imagine the wing in a wind tunnel -Air approaches the wing at speed v -Streamlines go about and below the wing -The wing is designed so air moves over the top faster than around the bottoms (higher speed air= lower pressure) -Just around the wing a clockwise circulation occurs and the flow is rotational -All o
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