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Chapter 15 Human Movement in a Fluid Medium Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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15-2 The Nature of Fluids What 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 body Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-3 The Nature of Fluids What is relative velocity? (velocity of a body with respect to the velocity of something else, such as the surrounding fluid) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-4 The Nature of Fluids v c/w = v c - v w Velocity of cyclist relative to wind (20 m/s) Cyclists velocity (15 m/s) Head wind velocity (5 m/s) Tail wind velocity (5 m/s) Velocity of cyclist relative to wind (10 m/s) Cyclists velocity (15 m/s) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-5 The Nature of Fluids What is laminar flow? Laminar flow is characterized by smooth, parallel layers of fluid. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-6 The Nature of Fluids What is turbulent flow? Turbulent flow is characterized by mixing of adjacent fluid layers. Region of turbulence Motion of sphere Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-7 The Nature of Fluids What are relevant fluid properties? density - mass/volume specific weight - weight/volume viscosity - internal resistance of a fluid to flow Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-8 Buoyancy What is buoyancy? a fluid force with: magnitude based on Archimedes principle, direction always vertically upward, and point of application being a bodys center of volume. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-9 Buoyancy What 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: F b = V d Where F b = buoyant force, V d = displaced fluid volume, = fluid specific weight Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-10 Buoyancy What 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, 6 th edition By Susan J. Hall, Ph.D.

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15-11 Buoyancy What determines whether a body floats or sinks? The equation of static equilibrium for vertical force can be used to quantitatively answer this question: F v = 0 0 = V - wt Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-12 Buoyancy A 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. A B Buoyant force Center of volume Weight Center of gravity Center of volume Buoyant force Center of gravity Weight Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-13 Drag What 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 fluid Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-14 Drag What factors affect the total drag force? Where: F D = drag, C D = the coefficient of drag - a unitless number; an index of a bodys ability to generate fluid resistance = fluid density A p = body surface area perpendicular to the fluid flow v = relative velocity of the body with respect to the fluid F D = ½C D A p v 2 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-15 Drag From 0 to v 1 drag increases approximately with velocity squared (v 2.) At v 1 there is sufficient relative velocity to generate a turbulent boundary layer, which is why, from v 1 to v 2, form drag decreases. After v 2, total drag increases. v1v1 v2v2 Relative velocity Drag force Laminar Turbulent Pattern of change in drag force with increasing relative velocity. Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-16 Drag What is skin friction? drag derived from friction in adjacent layers of fluid near a body moving through the fluid AKA surface drag and viscous drag Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-17 Drag What 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 layer Turbulent boundary layer Fluid flow Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-18 Drag What 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, 6 th edition By Susan J. Hall, Ph.D.

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15-19 Drag What 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 turbulence Motion of sphere Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-20 Drag What 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.) A B Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-21 Drag What 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 flow Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-22 Drag What is wave drag? (drag derived from the generation of waves at the interface between two different fluids, such as air and water) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-23 Drag What 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 fluid Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-24 Lift What 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 fluid Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-25 Lift What factors affect lift force? Where: F L = lift, C L = the coefficient of lift - a unitless number; an index of a bodys ability to generate lift = fluid density A P = body surface area perpendicular to the fluid flow v = relative velocity of the body with respect to the fluid F L = ½C L A p v 2 Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-26 Lift What 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, 6 th edition By Susan J. Hall, Ph.D.

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15-27 Lift What 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 pressure Low velocity high pressure Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-28 Lift What 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 pressure Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-29 Lift What is the Bernouli principle? Where: p = pressure, = specific weight of the fluid, z = elevation, v = relative velocity, g = acceleration of gravity, and C = a constant P v 2 + z + 2g = C Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-30 Lift What is the angle of attack? (angle between the longitudinal axis of a body and the direction of the fluid flow) Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-31 Lift What is the Magnus effect? deviation in the trajectory of a spinning object toward the direction of spin results from the Magnus force Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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15-32 Lift What is the Magnus force? Magnus force results from a pressure differential created by a spinning body. Relative low velocity flow Relative high pressure Relative high velocity flow Relative low pressure Magnus force Relative low velocity flow Relative high pressure Relative high velocity flow Relative low pressure Magnus force Topspin Backspin Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D.

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