1Fluid Mechanics• Fluid Mechanics: the study of forces that develop when an object moves through a fluid medium.• Two fluids of interest– Water–Air• In some cases, fluid forces have little effect on an object’s motion (e.g., shotput)• In other cases, fluid forces are significant– badminton, baseball, swimming, cycling, etc.• Three major fluid forces of interest:– Buoyancy–Drag–LiftFluid forces2Drag and Lift• The drag force acts in a direction that is opposite of the relative flow velocity.– Affected by cross-section area (form drag)– Affected by surface smoothness (surface drag)• The lift force acts in a direction that is perpendicular to the relative flow. – The lift force is not necessarily vertical.Vboat= 0Relative Velocity: IVwater= +10Vboat–Vwater= 0 – 10 = –10DRAG3Vboat= 10Relative Velocity: IIVwater= +10Vboat–Vwater= 10 – 10 = 0Vboat= 10Relative Velocity: IIIVwater= 0Vboat–Vwater= 10 – 0 = 10DRAG4Drag• Resistive force acting on a body moving through a fluid (air or water). Two types:– Surface drag: depends mainly on smoothness of surface of the object moving through the fluid.• shaving the body in swimming; wearing racing suits in skiing and speedskating.– Form drag: depends mainly on the cross-sectional area of the body presented to the fluid• bicyclist in upright v. crouched position• swimmer: related to buoyancy and how high the body sits in the water. – When would you want to increase drag?What does drag look like?FCAvDD=ρ225Lift• Represents a net force that acts perpendicular to the direction of the relative motion of the fluid; • Created by different pressures on opposite sides of an object due to fluid flow past the object– example: Airplane wing (hydrofoil)• Bernoulli’s principle: velocity is inversely proportional to pressure.– Fast relative velocity lower pressure– Slow relative velocity higher pressureWhat does lift look like?FCAvLL=ρ226Examples• Baseball: curveball, slider• Golf: slice, hook• Tennis: top-spin forehand• Autoracing: downforce• Soccer: “bender”• Volleyball: top-spin jumpservetop-spinflowNET FORCE (down)–10 m/s+2 m/s–2 m/slow relative air speed, high pressure area–8 m/shigh relative air speed, low pressure area–12 m/s7Volleyball: topspin serve1) Spin 2) Drag Force 3) Lift ForceThe Magnus Effect• The Magnus effect describes the curved path that is observed by spinning projectiles.– Explained by Bernoulli’s principle and the pressure differences caused by relative differences in flow velocities.8Explaining lift and drag• The drag force acts in a direction that is opposite of the relative flow velocity (i.e., it opposes the relative flow)– Affected by surface area (form drag)– Affected by surface smoothness (surface drag)• The lift force acts in a direction that is perpendicular to the relative flow. – The lift force is not necessarily vertical.Bernoulli’s PrincipleflowFaster AirflowSlower AirflowLower PressureHigher PressureLIFT9Newton’s Third LawflowLIFTAir forced down by wingWing forced up by airBuoyancy• Associated with how well a body floats or how hight it sits in the fluid.• Archimede’s principle: any body in a fluid medium will experience a buoyant force equal to the weight of the volume of fluid which is displaced.– Example: a boat on a lake. A portion of the boat is submerged and displaces a given volume of water. The weight of this displaced water equals the magnitude of the buoyant force acting on the boat. – The boat will float if its weight in air is less than or equal to the weight of an equal volume of water.• Buoyancy is closely related to the concept of density.Density = mass/volume10Example: Underwater weighing• Body composition assessment using the underwater weighing technique is common application of Archimede’s principle.– Human body is composed of varying amounts of muscle, bone, and fat.– Densities of:• Fat: 0.95 g/cm3• Muscle: 1.05-1.10 g/cm3• Bone: 1.4-1.9 g/cm3– Underwater weighing provides a direct estimate of average body density. Prediction equations then allow for estimation of %fat and %lean body mass.Center of buoyancy & swimming performanceWeight: Center of massBuoyant force:Center of buoyancyDRAGd17Center of buoyancyDRAGIncreased tilt in water results in greater form drag! This decreases efficiency!Research has shown that men have a greater dthan women. This creates a greater “feet-sinking torque”.It has been suggested that this is a bigger problem for men than for women -