ES 202 Fluid and Thermal Systems Lecture 30: Lift and Drag Wrap-Up (2/20/2003)

1. ES 202Fluid and Thermal SystemsLecture 30:Lift and Drag Wrap-Up(2/20/2003)

2. Assignments • Study for your finals ES 202 Fluid & Thermal Systems

3. Announcements • Problem session this evening at 7 pm • lift and drag • hydrostatics • Bernoulli’s equation • major and minor losses • Time and date for final review session (need your input) • What can you bring to the exam • textbook • 3 sides of equation sheet • computer (cannot use EES) • My advice for you on final exam • Study hard, see me if you have questions • Keep calm! You should have more than enough time! ES 202 Fluid & Thermal Systems

4. Road Map of Lecture 30 • High-light from John Adams’ talk on golf ball aerodynamics • laminar-turbulent transition over curved surface • Reynolds number dependency of drag coefficient • how it relates to terminal velocity calculation • Common feature between internal and external flows • formation of boundary layer • inviscid core region • merging of boundary layers (disappearance of inviscid core) • Visual learning: variation of lift and drag with angle of attack • All about lift • origin of lift • definition of lift coefficient • conditions at take-off and cruise • Course evaluation ES 202 Fluid & Thermal Systems

5. Drag on a Golf Ball 2/3 of range at max. height (very different from simple projectile) Taken from John Adams’ ASME talk ES 202 Fluid & Thermal Systems

6. Determination of terminal velocity requires iteration Reynolds Number Dependency taken from Figure 8.2 in Fluid Mechanics by Kundu ES 202 Fluid & Thermal Systems

7. Connection with Internal Flow • Recall the drag analysis on a cross-flow cylinder in a wind tunnel • The blockage effect of the cylinder causes the flow to accelerate. As a result, pressure drops. • This pressure drop is totally different from the pressure drop in pipe flow analysis during the 4th week of this class. • The pressure drop in pipe flow is due to frictional effect, not flow acceleration. • In fact, the average flow speed in a constant cross-sectional pipe is constant as a result of mass conservation. ES 202 Fluid & Thermal Systems

8. boundary layer inviscid core (flow acceleration) fully viscous region merging of boundary layer (disappearance of inviscid core) boundary layer Boundary Layer in a Pipe • At the pipe entrance, the development of boundary layer is similar to that on a flat plate. • As a result of fluid deceleration in the boundary layer, the flow accelerates within the inviscid core. • Beyond the merging point of boundary layers, the fully viscous region is termed the fully developed flow. • Within the fully developed flow, • averaged flow speed stays constant; • pressure drops as a response to fluid friction. ES 202 Fluid & Thermal Systems

9. Lift and Drag on an Airfoil • Visual learning: • MMFM visualization of lift and drag variation as a function of angle of attack (serves as a motivation to lift analysis) • As the angle of attack is increased, the slender airfoil becomes more of a blunt body.Flow separation becomes more severe. • The dominant drag component changes from frictional drag to pressure drag. • Significant reduction in lift results. • Notion of stall: large reduction in lift (highly unstable operating condition) ES 202 Fluid & Thermal Systems

10. All about Lift • Generation of lift force • high pressure on bottom surface, low pressure on top surface • means of destroying flow symmetry • non-zero angle of attack on symmetry airfoil • asymmetric airfoil at zero angle of attack • positive camber gives positive lift • Design criterion of airfoil design • optimize the lift-to-drag ratio • Lift coefficient • definition (similar to drag coefficient) • take-off condition (L > W) • cruise condition (L = W) ES 202 Fluid & Thermal Systems