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A cylinder is falling through a fluid at Velocity V

Fluid Forces: Chapters 9 and 11: Section 1--Overview. A cylinder is falling through a fluid at Velocity V. What are the Forces Acting?. Buoyancy. Would you expect the force Acting to be a function of Velocity?. Weight. V. There is a pressure Difference between back and

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A cylinder is falling through a fluid at Velocity V

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  1. Fluid Forces: Chapters 9 and 11: Section 1--Overview A cylinder is falling through a fluid at Velocity V What are the Forces Acting? Buoyancy Would you expect the force Acting to be a function of Velocity? Weight V There is a pressure Difference between back and front –leads to an additional force called DRAG Drag Force—function of Velocity and “projected Area” Net Force: A dimensionless Coef, free stream velocity— vel. relative to object In same direction as Drag Area projected in flow direction (a circle here) A Common Form

  2. So Drag is a result of fluid moving over a body—Are there other forces that can arise in this way Flow over a thin plate—Drag not important Buoyancy Small projected area But fluid will impose a shear stress —recall pipe friction— on Surface of plate Weight V Resulting in a Surface Resistance Forcein direction of free stream velocity Net Force: Surface area (parallel to flow) Dimensionless coef. What Area here?

  3. Also Lift: Consider rotating Cylinder in Free stream Flow V V The Magnus Effect High Vel, Low p Why? Low Vel, Hight p Pressure Difference will lead to a Force— The Lift Force —NORMAL to free stream Direction—Engineers calculate this as plan area (looking down on flow) Dimensionless coef.

  4. So—there are three forces that can occur due to flow over a body In flow direction ------- normal to flow Drag Surface Resistance Lift Trick is finding C Also in tables For given Bodies Look up in tables Correlated to Account for Drag and shear resistance see next slide and later notes Can be calculated for plate See section 2

  5. Relation between Stress Distribution and Flow Forces (See Fig 11.2) Free-Stream Velocity V will give rise to pressure acting normal to body and shear acting along body Lift force normal to flow Drag force in line with flow form drag friction drag form drag friction drag One value for body and flow condition

  6. Section 2: Boundary Layers—Calculating Surface Resistance

  7. Drag on a surface – 2 types • Pressure stress • Shear stress / skin friction drag Chapter 9

  8. Boundary layer – velocity profile • Far from the surface, the fluid velocity is unaffected. • In a thin region near the surface, the velocity is reduced • Which is the “most correct” velocity profile? …this is a good approximation near the “front” of the plate

  9. Boundary layer growth • The free stream velocity is u0, but next to the plate, the flow is reduced by drag • Farther along the plate, the affect of the drag is felt by more of the stream, and because of this the boundary layer grows • Fluid friction on the surface is associated with velocity reduction throughout the boundary layer

  10. Local stress & total force, skin friction • Not immediately straightforward (unlike approximations we made with thin films): • du/dy decreases with x & y • We need to find then • And there is more trouble… Breadth

  11. Boundary layer transition to turbulence At a certain distance along a plate, viscous forces become to small relative to inertial forces to damp fluctuations

  12. Picture of boundary layer from text figure_09_04 figure_09_04

  13. Boundary layer transition • How can we solve problems for such a complex system? • We can think about key parameters and possible dimensionless numbers • Important parameters: • Viscosity μ, density ρ • Distance, x • Velocity uO • Reynolds number combines these into one number δ(x)

  14. B L thickness in laminar region Self-similar shape

  15. Boundary layer questions • How can we solve problems for such a complex system? • We can think about key parameters and possible dimensionless numbers • What about stress? • We talk about (local) stress and (total) force on a boundary in terms of local cf and average CF stress coefficients: δ(x)

  16. Average shear-stress coefficientOn Plate of Length L Ignore this part just for a moment figure_09_12 Note New Reynolds No

  17. Example 9.6 from text • A plate is 3 m long x 1 m wide • Air at 20°C and atmospheric pressure flows past this plate with a velocity of 30 m/s • A boundary layer over a smooth, flat plate is laminar at first and then becomes turbulent. The turbulent forms of drag, etc., are reasonable above Re = 5 x 105. • What is the average resistance coefficient Cf for the plate? • Also, what will be the total shearing resistance force of one side of the plate? • What will be the resistance due to the turbulent part and the laminar part of the boundary layer?

  18. Find , shearing resistance on one side of plate, and resistance due to laminar flow Here it is !

  19. Find , shearing resistance on one side of plate, and resistance due to laminar flow 1st calculate plat Reynolds number Mixed laminar-Turbulent

  20. Find , shearing resistance on one side of plate, and resistance due to laminar flow

  21. Find , shearing resistance on one side of plate, and resistance due to laminar flow Now Calculate Transition point

  22. Find , shearing resistance on one side of plate, and resistance due to laminar flow Now Calculate Transition point So laminar layer Coefficient is

  23. Find , shearing resistance on one side of plate, and resistance due to laminar flow Now Calculate Transition point So laminar layer Coefficient is And laminar force is

  24. Average shear-stress coefficient figure_09_12

  25. Laminar, Turbulence, Induced Turbulence

  26. Back to drag on submerged objects…

  27. Drag on a surface – 2 types • Pressure stress / form drag • Shear stress / skin friction drag • A boundary layer forms due to skin friction • For shapes more complex than a plane, these result in total drag forces which are usually hard to solve analytically

  28. Shortcuts for total drag • For less precise design and/or well-known / well-studied (simple) objects, we rely on charts for an average coefficient of drag Frontal Area + shear

  29. Drag coefficients for 2d or infinitely long objects for 3d bodies figure_11_04 figure_11_07

  30. P 11.18, 9th edition Compute the overturning moment exerted by a 35 m/s wind on a smokestack that has a diameter of 2.5 m and a height of 75 m. Assume that the air temperature is 20° C and that the atmospheric pressure is 99 kPa absolute.

  31. 2.5 m V= 35m/s Object is ~an infinite cylinder 75m

  32. d=2.5 m V= 35m/s Object is ~an infinite cylinder 75m

  33. d=2.5 m V= 35m/s Object is ~an infinite cylinder 75m Then turning moment

  34. Lift

  35. Total lift • Similar to our calculations of total drag, we rely on charts for an average coefficient of lift • A is a reference area, usually “planform area”

  36. Example 11.6 Lift on a Rotating Sphere A ping-pong ball is moving at 10 m/s in air and is spinning CW at 6000 rpm as shown. The ball diameter = 3 cm. Calculate the lift and drag forces and indicate the direction of each. Assume standard atmospheric pressure and a temperature of 20 C. How does the answer change if the ball is spinning CCW? 6000 0.03 Rotation parameter

  37. Find Lift and Drag Forces on Ping-Pong 6000 0.03 Rotation rate Rotation parameter Rotation parameter

  38. So—there are three forces that can occur due to flow over a body In flow direction ------- normal to flow Drag Surface Resistance Lift Trick is finding C Also in tables ch 11 For given Bodies Look up in tables ch 11 Correlated to Account for Drag and shear resistance see next slide and later notes Can be calculated for plate See chapter 9

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