Bài giảng Basic Biomechanics - Chapter 15 Human Movement in a Fluid Medium

Chapter 15Human Movement in a Fluid MediumBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.© 2012 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinThe Nature of FluidsWhat is a fluid? a substance that flows or continuously deforms when subjected to a shear stress both liquids and gases are fluids air and water are fluids that commonly exert forces on the human bodyBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.The Nature of FluidsWhat is relative velocity?(velocity of a body with respect to the velocity of something else, such as the surrounding fluid)Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.The Nature of Fluidsvc/w = vc- vwVelocity of cyclist relative to wind (20 m/s)Cyclist’s velocity (15 m/s)Head windvelocity(5 m/s)Tail windvelocity(5 m/s)Velocity of cyclist relative to wind (10 m/s)Cyclist’s velocity (15 m/s)Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.The Nature of FluidsWhat is laminar flow?Laminar flow is characterized by smooth, parallel layers of fluid.Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.The Nature of FluidsWhat is turbulent flow?Turbulent flow is characterized by mixing of adjacent fluid layers.Region of turbulenceMotion of sphereBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.The Nature of FluidsWhat are relevant fluid properties? density - mass/volume specific weight - weight/volume viscosity - internal resistance of a fluid to flowBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.BuoyancyWhat is buoyancy?a fluid force with: magnitude based on Archimedes’ principle, direction always vertically upward, and point of application being a body’s center of volume.Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.BuoyancyWhat is Archimedes’ principle?A physical law stating that the buoyant force acting on a body is equal to the weight of the fluid displaced by the body: Fb = VdWhere Fb = buoyant force, Vd = displaced fluid volume,  = fluid specific weightBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.BuoyancyWhat determines whether a body floats or sinks? Floating occurs when the buoyant force is greater than or equal to body weight. Sinking occurs when body weight is greater than the buoyant force.Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.BuoyancyWhat determines whether a body floats or sinks?The equation of static equilibrium for vertical force can be used to quantitatively answer this question: Fv = 0 0 = V - wtBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.BuoyancyA floating body at rest (position A) will rotate until the buoyant force and weight force are vertically aligned (position B) so that zero torque is present.ABBuoyantforceCenter ofvolumeWeightCenter ofgravityCenter ofvolumeBuoyantforceCenter ofgravityWeightBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is drag? a force caused by the dynamic action of a fluid that acts in the direction of the freestream fluid flow generally a resistance force that tends to slow the motion of a body moving through a fluidBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat factors affect the total drag force?Where: FD = drag, CD = the coefficient of drag - a unitless number; an index of a body’s ability to generate fluid resistance  = fluid density Ap = body surface area perpendicular to the fluid flow v = relative velocity of the body with respect to the fluid FD = ½CDApv2Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragFrom 0 to v1 drag increases approximately with velocity squared (v2.) At v1 there is sufficient relative velocity to generate a turbulent boundary layer, which is why, from v1 to v2, form drag decreases. After v2, total drag increases.v1v2Relative velocityDrag forceLaminarTurbulentPattern of change in drag force with increasing relative velocity.Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is skin friction? drag derived from friction in adjacent layers of fluid near a body moving through the fluid AKA surface drag and viscous dragBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is skin friction?Side view of fluid flow around a flat thin plate. Skin friction is the form of drag that predominates when the flow is primarily laminar.Laminar boundary layerTurbulent boundary layerFluid flowBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat factors affect the magnitude of skin friction?Skin friction increases with: the relative velocity of fluid flow the surface area of the body over which the flow occurs the roughness of the body surface the viscosity of the fluid Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is form drag?Form drag is derived from a pressure differential between the lead and rear sides of a body moving through a fluid. It is also known as profile drag and pressure drag.Region of turbulenceMotion of sphereBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is form drag?A streamlined shape (A) reduces form drag by reducing the turbulence created at the trailing edge, (thus reducing the pressure differential present in B.)ABBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat factors affect the magnitude of form drag?Form drag increases with: the relative velocity of fluid flow the magnitude of the pressure gradient between the front and rear ends of the body the surface area of the body perpendicular to the fluid flowBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat is wave drag?(drag derived from the generation of waves at the interface between two different fluids, such as air and water)Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.DragWhat factors affect the magnitude of wave drag?Wave drag increases with: the vertical oscillation of the body with respect to the fluid the relative velocity of the body in the fluidBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is lift? a force acting on a body in a fluid in a direction perpendicular to the fluid flow generally a resistance force that tends to slow the motion of a body moving through a fluidBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat factors affect lift force?Where: FL = lift, CL = the coefficient of lift - a unitless number; an index of a body’s ability to generate lift  = fluid density AP = body surface area perpendicular to the fluid flow v = relative velocity of the body with respect to the fluid FL = ½CLApv2Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat factors affect the magnitude of lift?Lift increases with: the relative velocity of fluid flow the surface area of the flat side of the foil the coefficient of lift the density of the fluid Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is a foil?(a shape capable of generating lift in a fluid)Lift generated by a foil is directed from the region of relative high pressure on the flat side of the foil toward the region of relative low pressure on the curved side of the foil.High velocity low pressureLow velocity high pressureBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is the Bernouli principle? an expression of the inverse relationship between relative velocity and relative pressure in a fluid flow regions of low relative velocity are associated with relative high pressure regions of high relative velocity are associated with relative low pressureBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is the Bernouli principle?Where: p = pressure,  = specific weight of the fluid, z = elevation, v = relative velocity, g = acceleration of gravity, and C = a constantP v2 + z + 2g = CBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is the angle of attack?(angle between the longitudinal axis of a body and the direction of the fluid flow)Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is the Magnus effect? deviation in the trajectory of a spinning object toward the direction of spin results from the Magnus forceBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.LiftWhat is the Magnus force?Magnus force results from a pressure differential created by a spinning body.Relative low velocity flowRelative high pressureRelative high velocity flowRelative low pressureMagnusforceRelative low velocity flowRelative high pressureRelative high velocity flowRelative low pressureMagnusforceTopspinBackspinBasic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.