ES 202 Fluid and Thermal Systems Lecture 29: Drag and Lift Coefficients (2/18/2003)

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ES 202Fluid and Thermal SystemsLecture
29Drag and Lift Coefficients(2/18/2003)
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Assignments

• Homework
• 13-56C, 13-62, 13-63, 13-72C, 13-88
• Reading
• 13-7 to 13-8

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Announcements

• Guest speaker Dr. John Adams will talk 2 talks
  today
• Hypersonic Systems, Technology, and Testing,
  including relevant remarks on the recent Columbia
  Space Shuttle tragedy in O259 at 420 pm
• Flight Mechanics of a Spinning Dimpled Spheroid
  in the Khan Room at 600 pm
• Homework assigned this week is just for your
  learning, no need to hand it in

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Road Map of Lecture 29

• Finish up example on drag coefficient of
  cross-flow cylinder in a wind tunnel
• Give out answers to in-class drag analyses
  yesterday
• Introduce definition of drag coefficients
• (Combined) Drag coefficients for objects of
  various geometries
• concept of streamlining
• Categorization of drag components
• skin frictional drag versus pressure drag
• effects of body shape on drag (blunt body versus
  slender body)
• flow separation (an artifact of fluid viscosity)
• Exercise on qualitative description of flow
  acceleration and pressure variation over a blunt
  body
• notion of stagnation point (high pressure)
• Applications
• truck tipping problem

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Answers to Drag Analyses

• Drag analysis on a flat plate
• Drag analysis on a cross-flow cylinder in open
  air
• Drag analysis on a cross-flow cylinder in a wind
  tunnel

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Drag Coefficient

• From the results of drag analysis on a cross-flow
  cylinder in open air,
• a non-dimensional group, the drag coefficient CD
  , can be defined
• The definition of drag coefficient can also be
  arrived by means of dimensional analysis, similar
  to that on boundary layer thickness.
• Show drag coefficient tables for various
  geometries

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Categorization of Drag Components

• The total drag force on an object can be broadly
  classified into two categories

Total drag force

• Friction drag
• directly related to
• skin friction on surfaces
• dominant on slender bodies

• Pressure (form) drag
• indirectly related to fluid viscosity
• due to momentum losses through viscosity
• mostly involves flow separation
• dominant on blunt bodies

• Relative importance between friction drag and
  pressure drag is strongly Reynolds number
  dependent and geometry dependent (slender versus
  blunt bodies).

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Fluid Acceleration and Pressure Variation

• Perform a qualitative assessment on the changes
  in a flow as it approaches a blunt object.

• speed decreases, pressure increases from
  free-stream to stagnation point
• highest pressure at stagnation point
• flow splits into upper and lower streams
• speed increases, pressure decreases from
  stagnation point to edges
• highest speed and lowest pressure at the edges
• flow speed decreases and pressure recovers behind
  the object
• too much momentum loss in boundary layer not
  enough momentum to negotiate pressure hill, flow
  separates
• large pressure difference between front and back
  sides causes pressure drag

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Example Problem

• Truck tipping problem

• recognize blunt body geometry
• pressure drag as dominant drag component
• moment analysis about Point O to determine
  minimum wind speed to tip truck
• assume drag coefficient is all attributed to
  pressure drag
• assume line of action of pressure drag to be at
  the geometrical center of truck
• at tipping position, R2 0
• fine points
• small frictional drag component in tabulated CD
  value
• asymmetry in problem not accounted for in
  tabulated CD value

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Terminal Speed of Falling Objects

• Identify the major forces on a falling object

• As the falling object accelerates, the drag force
  increases rapidly (quadratic dependence on
  falling speed).
• At terminal speed, the net force on the falling
  object is zero, implying a perfect balance
  between body weight and drag.
• The force balance sets the condition to determine
  the terminal speed.