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ES 202 Fluid and Thermal Systems Lecture 26: Friction Drag on a Flat Plate (2/11/2003)

ES 202 Fluid and Thermal Systems Lecture 26: Friction Drag on a Flat Plate (2/11/2003). Assignments. Homework: 13-41C, 13-47, 13-54 Look up values of m, r, n for air and water Reading: 13-1 to 13-6. Announcements. Feedback on Exam 2 duration degree of difficulty

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ES 202 Fluid and Thermal Systems Lecture 26: Friction Drag on a Flat Plate (2/11/2003)

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  1. ES 202Fluid and Thermal SystemsLecture 26:Friction Drag on a Flat Plate(2/11/2003)

  2. Assignments • Homework: • 13-41C, 13-47, 13-54 • Look up values of m, r, n for air and water • Reading: • 13-1 to 13-6 ES 202 Fluid & Thermal Systems

  3. Announcements • Feedback on Exam 2 • duration • degree of difficulty • Write-up for Lab 3 due on Friday • one write-up per lab group • analysis on four data sets ES 202 Fluid & Thermal Systems

  4. Road Map of Lecture 26 Knowledge items: • Origin of viscous drag • recall fluid friction (i.e. viscosity) • no-slip condition at boundaries (kinematic condition) • concept of boundary layer (region of significant viscous effects) • Laminar-turbulent transition in boundary layer • Drag on a flat plate Visual learning: • Visualizations from MMFM Applications: • Dimensional analysis of boundary layer thickness on flat plate • Control volume analysis of flat plate boundary layer ES 202 Fluid & Thermal Systems

  5. Internal Versus External Flows • Application of fluid mechanics can be broadly classified into two categories: Applications of Fluid Mechanics • Internal flows • pipe flow • channel flow • External flows • flat plate • cylinders, spheres • airfoils ES 202 Fluid & Thermal Systems

  6. Recall Fluid Friction • Fluid friction • also termed “viscosity” • basketball-tennis-ball demonstration • exchange of momentum at the molecular scales • no-slip conditions at the solid surface (imagine thin layers of fluid moving relative to one another) • concept of boundary layer • stress-strain relation in a Newtonian fluid stress = viscosity X strain rate ES 202 Fluid & Thermal Systems

  7. Concept of Boundary Layer • Due to the no-slip boundary condition (a kinematic condition), the layer of fluid immediately adjacent to the flat plate is not moving. • The fluid which is far away from the flat plate does not “feel” the presence of the plate and travels at the free-stream speed (U). • Between the plate surface and free-stream, the fluid velocity changes from zero (plate surface) to the free-stream speed over a thin region. • Show MMFM visualization • This thin region is termed the “boundary layer”. ES 202 Fluid & Thermal Systems

  8. propagation direction of viscous effects flow direction Features of Boundary Layer • Due to the “thinness” of the boundary layer, the velocity gradientis LARGE. • Hence, viscous effects are important there. Why? • Never apply Bernoulli’s equation in the boundary layer. Why? • Effects in two different directions: • flow is convected in the streamwise direction • presence of the flat plate is propagated in the normal direction into the fluid • Result: boundary layer thickness grows in the streamwise direction. • Exercise: Perform dimensional analysis on boundary layer thickness. ES 202 Fluid & Thermal Systems

  9. Laminar-Turbulent Transition • Similar to the laminar-turbulent transition in pipe flow, the flow over a flat plat also experiences a transition from laminar state to turbulent state when the local Reynolds number ( Rex ) exceeds a critical number. • The critical value can be taken to be • In reality, the nominal critical Reynolds number depends on a host of different factors like level of free-stream disturbance,surface roughness,etc. Its exact value can vary over a large range. Taken from Multi-Media Fluid Mechanics (Homsy et al.) ES 202 Fluid & Thermal Systems

  10. Significance of Reynolds Number • Definition of Reynolds number: • The Reynolds number can be interpreted as the ratio of inertial to viscous effects (one of many interpretations) • At low Reynolds number, • viscous effect is comparable to inertial effect • flow behaves in orderly manner (laminar flow) • At high Reynolds number, • viscous effect is insignificant compared with inertial effect. • flow pattern is irregular, unsteady and random (turbulent flow) ES 202 Fluid & Thermal Systems

  11. Scaling of Boundary Layer Thickness • In the laminar regime (close to the leading edge), • In the turbulent regime (beyond transition point): ES 202 Fluid & Thermal Systems

  12. Drag on a Flat Plate • Due to viscous (fluid friction) effects, the flat plate will experience a force in the downstream direction. The force is termed “Drag”. • Think of it as an action-reaction pair of force: • the fluid experiences a force in the upstream direction to slow it down; • the same force (in magnitude) acts on the flat plate in opposite direction. • Exercise: Perform a control volume analysis on a flat plate to find out its total drag. • Suggest another way to find the drag on a flat plate. ES 202 Fluid & Thermal Systems

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