Fluid Mechanics Liquids and gases have the ability to flow They are called fluids There are a variety of “LAWS” that fluids obey Need some definitions

Fluid Mechanics Fluid Mechanics: the study of forces that develop when an object moves through a fluid medium. Two fluids are of interest – Water – Air

Fluid forces 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 are of interest: – Buoyancy – Drag – Lift

Drag 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.

Drag 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 speed skating. – 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?

Lift 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 across the object – example: Discus face turns downward Bernoulli’s principle: velocity is inversely proportional to pressure. – Fast relative velocity lower pressure – Slow relative velocity higher pressure

Examples Baseball: curveball, Golf: slice, Tennis: top-spin forehand, Slice Soccer: Curved corner kick Volleyball: top-spin jump serve

The 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 a moving fluid.

Bernoulli’s Principle Faster Airflow Lower Pressure Slower Airflow Higher Pressure

Buoyancy Associated with how well a body floats or how high 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.

Buoyancy 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/volume Specific Gravity = Body Weight/Displaced water weight

Buoyancy A ratio of greater than 1 exhibits that the body will sink because the body weight is more than the displaced water. A ratio of less than 1 designate that the body will float because the displaced water weight is more than the weight of body.

Example: 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: g/cm3 Bone: 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 Increased tilt in water results in greater form drag! This decreases efficiency! Research has shown that men have a greater drag than women. This creates a greater “feet sinking torque”. It has been suggested that this is a bigger problem for men than for women.

Density & Pressure Density : Regardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space. Pressure : A measure of the amount of force exerted on a surface area.

Pressure in a Fluid The pressure is just the weight of all the fluid above you Atmospheric pressure is just the weight of all the air above on area on the surface of the earth In a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water)

Pressure in a Fluid So, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE you The deeper you go, the more weight above you and the more pressure Go to a mountaintop and the air pressure is lower

Pressure Concept Pressure acts perpendicular to the surface and increases at greater depth.

Buoyancy Net upward force is called the buoyant force!!! Easier to lift a rock in water!!

Displacement of Water The amount of water displaced is equal to the volume of the rock.

Archimedes’ Principle An immersed body is buoyed up by a force equal to the weight of the fluid it displaces. If the buoyant force on an object is greater than the force of gravity acting on the object, the object will float The apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

Flotation A floating object displaces a weight of fluid equal to its own weight.

Flotation Example

Principles of Fluid Flow The continuity equation results fromconservation of mass. Continuity equation: A1v1 = A2v2 Area x speed in region 1 = area x speed in region 2

Bernoulli’s Principle Flow is faster when the pipe is narrower

Bernoulli’s Principle When the speed of a fluid increases, internal pressure in the fluid decreases.

Principles of Fluid Flow The speed of fluid flowdepends on crosssectionalarea. Bernoulli’s principle states that the pressurein a fluid decreases as the fluid’s velocity increases.

Factors to be Controlled for Reducing Water Resistance Waves Eddies Cavitation Skin Friction (Surface Drag) Starting and stopping force Force applied on unproductive angle Form drag Internal Resistance