4/12/11 Pressure Gradients in Boundary Layer Flow Class 23 – Fluid Mechanics Tuesday, April 12th Boundary Layer SeparaCon Boundary Layer SeparaCon 1 4/12/11 For a body which is symmetric about flow direcCon, what is the drag force? a)  Zero b)  Non-­‐zero Drag Drag – a net force in the direcCon of the flow due to pressure and shear stress forces Two types: 1.  fricCon drag 2.  pressure (form) drag For a body which is symmetric about flow direcCon, what is the liO force? a)  Zero b)  Non-­‐zero Drag Coefficient with or 2 4/12/11 Drag Drag 1.  Pure FricCon Drag: Flat Plate Parallel to the Flow 1.  Flow over a Flat Plate Parallel to the Flow: FricCon Drag 2.  Pure Pressure Drag: Flat Plate Perpendicular to the Flow 3.  FricCon and Pressure Drag: Flow over a Sphere and Cylinder Drag 1.  Flow over a Flat Plate Parallel to the Flow: FricCon Drag Boundary Layer can be 100% laminar, partly laminar and partly turbulent, or essenCally 100% turbulent; hence several different drag coefficients are available Drag 2.  Flow over a Flat Plate Perpendicular to the Flow: Pressure Drag Laminar BL: Turbulent BL: … plus others for transiConal flow 3 4/12/11 Drag 3.  Flow over a Sphere and Cylinder: FricCon and Pressure Drag Drag For what aspect raCo will fricCon drag be greater than pressure (form) drag? a)  l/D -­‐> ∞ b)  l/D -­‐> 0 A sphere of diameter D and density ρs falls at a steady rate through a liquid of density ρ and viscosity μ. If the Reynolds number is less than 1 show that the viscosity can be determined from μ = gD2(ρs – ρ)/18U. 4 4/12/11 A sphere of diameter D and density ρs falls at a steady rate through a liquid of density ρ and viscosity μ. If the Reynolds number is less than 1 show that the viscosity can be determined from μ = gD2(ρs – ρ)/18U. Drag Coefficients – 2D Drag Coefficients – 2D Drag Coefficients – 3D 5 4/12/11 Drag Coefficients – 3D Drag Coefficients Drag Coefficients A 22in by 34 in speed limit sign is supported on a 3in wide, 5O long pole. EsCmate the bending moment in the pole at ground level when a 30mph wind blows against the sign. video 6 4/12/11 A 22in by 34 in speed limit sign is supported on a 3in wide, 5O long pole. EsCmate the bending moment in the pole at ground level when a 30mph wind blows against the sign. Streamlining By appropriate streamlining, the drag coefficient for an airplane is reduced by 18% while the frontal area remains the same. For the same power output, by what percentage is the flight speed increased? LiO 7 4/12/11 LiO LiO Examples: NACA 23015; NACA 662-­‐215 A Boeing 747 aircraO weighing 580,000lbs when loaded with fuel and 100 passengers takes off with an airspeed of 140mph. With the same configuraCon, what is its takeoff speed if it is loaded with 372 passengers. Assume each passenger with luggage weighs 200lb. 8