# ch76b - Chapter 7 Flow Past Immerses Bodies 7.1 7.2 7.3 7.4...

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Chapter 7: Flow Past Immerses Bodies 7.1 Reynolds Number and Geometry Effects 7.2 Momenum Integral Estimates 7.3 The Boundary Layer Equations 7.4 The Flat Plate Boundary Layer 7.5 Boundary Layers with Pressure Gradients 7.6 Experimental External Flows Forces on Lifting Bodies

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FORCES ON LIFTING BODIES NASA - Helios Want large force normal to free stream(lift) and small force parallel (drag) to free stream. Conventional shape like bird’s wing, with t/c 0.24 and rounding leading edge and sharp trailing edge (subsonic).
“Dissect the bat, study it carefully, and on this model construct the machine.” Leonardo da Vinci 1505 Ornithopter by da Vinci (1490) 1891 – first successful heavier than air flying machine hang glider of Otto Lilienthal

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For most objects moving through a fluid, the significant fluid force is drag. However for some specially shaped* objects the lift force is also important. LIFT C L C D * can develop lift at angle of attack
LIFT lower pressure suction higher pressure An object moving horizontally will experience lift if that object produces an asymmetrical (top-to-bottom) flow field.

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Forces on airplane at level speed and constant height and speed. Lift force is the component of R that is perpendicular to free stream velocity , and drag is the component of R parallel to the free stream velocity. If planes height is not changing then: Lift = Weight
F L F D Note: F L is not parallel to N but perpendicular to V c = chord line = distance from leading edge to trailing edge (if c is not line of symmetry than wing is cambered) α = angle of attack = angle between free stream and chord line

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C L = F L /( 1 / 2 ρ V 2 A p ) C D = F D /( 1 / 2 ρ V 2 A p ) {C D for most bodies ( other than airfoils, hydrofoils, vanes ) is usually based on the frontal area.} A p A p and c are independent of α A p = planform area max. proj. of wing For low-speed flow with a given roughness ratio: C L = f( α ,Re c ); C D = f( α ,Re c ) A p not function of α
If camber (mean) line and chord line do not overlap, h 0, then airfoil is cambered. Typically t/c 0.24; rounded leading edge prevents separation; sharp trailing edge causes tangential wake motion that produces lift. h is the maximum camber

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LIFT: Example – flat plate The kite was first developed in China around 1000 BC. It appeared much later (1300) in Europe in the shape of a windsock. The first known illustration of the more conventional plane-surface diamond shape dates back to 1618.