Illinois State University Chapter 8 ä Fluid Mechanics ä The Effects of Water and Air.

Illinois State UniversityIllinois State University

Chapter 8Chapter 8

Fluid MechanicsFluid Mechanics

The Effects of Water and AirThe Effects of Water and Air


FluidFluid

Substance that flows when subjected to a Substance that flows when subjected to a shear stress.shear stress.

Both air and water are fluid mediums that Both air and water are fluid mediums that exert forces on bodies moving through exert forces on bodies moving through them.them.


FluidFluid

Both gases and liquids are fluids with Both gases and liquids are fluids with similar mechanical properties.similar mechanical properties.


Forces in a Fluid EnvironmentForces in a Fluid Environment

Two types of forces are exerted on an Two types of forces are exerted on an object by a fluid environment”object by a fluid environment” a a buoyant force buoyant force due to its immersion in the due to its immersion in the

fluid and,fluid and, a a dynamic force dynamic force due to its relative motion in the due to its relative motion in the

fluid.fluid.


BuoyancyBuoyancy

A fluid force that always acts vertically A fluid force that always acts vertically upward.upward.


Archimedes’ PrincipleArchimedes’ Principle

Physical law stating that the buoyant force Physical law stating that the buoyant force acting on a body is equal to the weight of acting on a body is equal to the weight of the fluid displaced by the body.the fluid displaced by the body.


VolumeVolume

VolumeVolume - amount of space occupied by a - amount of space occupied by a body. body.

In the metric system, common units of In the metric system, common units of volume are cubic centimeters (cmvolume are cubic centimeters (cm33), m), m33, and , and liters. liters.

One l = 1000 cmOne l = 1000 cm33. . In the English system, we use inIn the English system, we use in33, ft, ft33, and , and

quart. quart.


VolumeVolume

Volume is not the same as weight or mass.Volume is not the same as weight or mass. An 8 kg shot and softball occupy An 8 kg shot and softball occupy

approximately the same volume of space, but approximately the same volume of space, but the weight of the shot is much greater than that the weight of the shot is much greater than that of the softball. of the softball.

If a lean, muscular individual and an obese If a lean, muscular individual and an obese person have identical body weights, the obese person have identical body weights, the obese person's body volume would be greater.person's body volume would be greater.


DensityDensity

DensityDensity - mass per unit volume. - mass per unit volume. Metric = kg/mMetric = kg/m33. . English does not usually use units of English does not usually use units of

density. density. Specific wt (wt per unit volume) is used Specific wt (wt per unit volume) is used

instead. instead.


DensityDensity

The shot has a greater density and specific The shot has a greater density and specific wt than a softball because the shot is wt than a softball because the shot is heavier. heavier.

A lean person with the same body weight as A lean person with the same body weight as an obese person has a higher body density an obese person has a higher body density because muscle is more dense than fat.because muscle is more dense than fat.


BuoyancyBuoyancy

Because the magnitude of the buoyant force Because the magnitude of the buoyant force is directly related to the volume of the is directly related to the volume of the submerged object, the point at which the submerged object, the point at which the buoyant force acts is the object’s buoyant force acts is the object’s center of center of volumevolume, which is also known as the , which is also known as the center center of buoyancyof buoyancy..


BuoyancyBuoyancy

The ability of a body to float in a fluid The ability of a body to float in a fluid medium depends on the relationship medium depends on the relationship between the body’s buoyancy and its between the body’s buoyancy and its weight.weight.


BuoyancyBuoyancy

In order for a body to float, the buoyant In order for a body to float, the buoyant force it generates must equal or exceed its force it generates must equal or exceed its weight.weight.

Some people float and other sink.Some people float and other sink. This difference in floatability is a function This difference in floatability is a function

of body density.of body density.


BuoyancyBuoyancy

The orientation of the human body as it The orientation of the human body as it floats in water is determined by the relative floats in water is determined by the relative position of the total body center of gravity position of the total body center of gravity relative to the total body center of volume.relative to the total body center of volume.


BuoyancyBuoyancy

The exact locations of the CG and CV vary The exact locations of the CG and CV vary with anthropometric dimensions and body with anthropometric dimensions and body composition.composition.

Typically the CG is inferior to the CV due Typically the CG is inferior to the CV due to the relatively large volume and relatively to the relatively large volume and relatively small weight of the lungs.small weight of the lungs.


BuoyancyBuoyancy

Because weight acts at the center of gravity Because weight acts at the center of gravity and buoyancy acts at the center of volume, and buoyancy acts at the center of volume, a torque is created that rotates the body a torque is created that rotates the body until it is positioned so that these two acting until it is positioned so that these two acting forces are vertically aligned and the torque forces are vertically aligned and the torque ceases to exist.ceases to exist.


Dynamic Fluid ForceDynamic Fluid Force

Force due to relative motionForce due to relative motion

When an object moves within a fluid (or When an object moves within a fluid (or when a fluid moves past an object when a fluid moves past an object immersed in it), dynamic fluid forces are immersed in it), dynamic fluid forces are exerted on the object by the fluid.exerted on the object by the fluid. Fire hose on riotersFire hose on rioters


Dynamic Fluid ForceDynamic Fluid Force

The dynamic fluid force is proportional to The dynamic fluid force is proportional to the the density of the fluiddensity of the fluid the surface area of the object immersed in the the surface area of the object immersed in the

fluidfluid the square of the relative velocity of the object the square of the relative velocity of the object

to the fluidto the fluid


Relative MotionRelative Motion

Because a fluid is a medium capable of Because a fluid is a medium capable of flow, the influence of the fluid on a body flow, the influence of the fluid on a body moving through it depends not only on the moving through it depends not only on the body’s velocity but also on the velocity of body’s velocity but also on the velocity of the fluid.the fluid. Swimming upstream and downstreamSwimming upstream and downstream


Relative velocityRelative velocity

Velocity of a body with respect to the Velocity of a body with respect to the velocity of something else, such as the velocity of something else, such as the surrounding fluid.surrounding fluid.


Relative velocityRelative velocity

The velocity of a body relative to a fluid The velocity of a body relative to a fluid influences the magnitude of the forces influences the magnitude of the forces exerted by the fluid on the body.exerted by the fluid on the body.


Flow propertiesFlow properties

Laminar flow Laminar flow - flow characterized by - flow characterized by smooth, parallel layers of fluid.smooth, parallel layers of fluid.


Flow propertiesFlow properties

Turbulent flow Turbulent flow - flow characterized by - flow characterized by mixing of adjacent fluid layers.mixing of adjacent fluid layers.


Fluid propertiesFluid properties

Others factors that influence the magnitude Others factors that influence the magnitude of the forces a fluid generates are the fluid’s of the forces a fluid generates are the fluid’s density, specific weight, and viscosity.density, specific weight, and viscosity.

DensityDensity is mass/volume. is mass/volume. Specific weight Specific weight is the ratio of weight to is the ratio of weight to

volume.volume.



The denser and heavier the fluid medium The denser and heavier the fluid medium surrounding a body, the greater the surrounding a body, the greater the magnitude of the forces the fluid exerts on magnitude of the forces the fluid exerts on the body.the body.

The property of The property of fluid viscosity fluid viscosity involves the involves the internal resistance of a fluid to flow.internal resistance of a fluid to flow.



The greater the extent to which a fluid The greater the extent to which a fluid resists flow under an applied force, the resists flow under an applied force, the more viscous the fluid is. more viscous the fluid is.

A thick molasses, for example, is more A thick molasses, for example, is more viscous that a liquid honey, which is more viscous that a liquid honey, which is more viscous than water.viscous than water.



Increased fluid viscosity results in increased Increased fluid viscosity results in increased forces exerted on bodies exposed to the forces exerted on bodies exposed to the fluid.fluid.



Atmospheric pressure and temperature Atmospheric pressure and temperature influence a fluid’s density, specific weight, influence a fluid’s density, specific weight, and viscosity.and viscosity.


DragDrag

A resistance force.A resistance force. A force that slows the motion of a body A force that slows the motion of a body

moving through a fluid.moving through a fluid.


Coefficient of DragCoefficient of Drag

Unitless number that is an index of a body’s Unitless number that is an index of a body’s ability to generate fluid resistance.ability to generate fluid resistance.

Depends on the shape and orientation of a Depends on the shape and orientation of a body relative to the fluid flow, with long, body relative to the fluid flow, with long, streamlined bodies generally having lower streamlined bodies generally having lower coefficients of drag than blunt or irregularly coefficients of drag than blunt or irregularly shaped objects.shaped objects.


Theoretical Square LawTheoretical Square Law

Drag increases approximately with the Drag increases approximately with the square of velocity when relative velocity is square of velocity when relative velocity is low.low.

According to this law, if cyclists double According to this law, if cyclists double their speed and other factors remain their speed and other factors remain constant, the drag force opposing them constant, the drag force opposing them increases fourfold.increases fourfold.


DragDrag

The effect of drag is more consequential The effect of drag is more consequential when a body is moving with high velocity, when a body is moving with high velocity, which occurs in sports such as cycling, which occurs in sports such as cycling, speed skating, downhill skiing, the bobsled speed skating, downhill skiing, the bobsled and luge.and luge.


DragDrag

Increase or decrease in the fluid density also Increase or decrease in the fluid density also results in proportional change in the drag results in proportional change in the drag force.force.


Skin frictionSkin friction

Skin friction is derived from the sliding Skin friction is derived from the sliding contacts between successive layers of fluid contacts between successive layers of fluid close to the surface of a moving body.close to the surface of a moving body.

It is also called surface drag and viscous It is also called surface drag and viscous drag.drag.



Several factors affect the magnitude of skin Several factors affect the magnitude of skin friction drag:friction drag:

It increases proportionally with increases in It increases proportionally with increases in the relative velocity of the fluid flow,the relative velocity of the fluid flow,

the surface area of the body over which the the surface area of the body over which the flow occurs,flow occurs,



the roughness of the body surface,the roughness of the body surface, and the viscosity of the fluid.and the viscosity of the fluid.



Wearing smooth, snug Wearing smooth, snug clothing helps to clothing helps to minimize skin friction.minimize skin friction.


Form dragForm drag

Resistance created by a pressure differential Resistance created by a pressure differential between the lead and rear sides of a body between the lead and rear sides of a body moving through a fluid.moving through a fluid.

Also called profile drag and pressure drag.Also called profile drag and pressure drag.


Form dragForm drag

Several factors affect the magnitude of form Several factors affect the magnitude of form drag including:drag including:

the relative velocity of the body with the relative velocity of the body with respect to the fluid,respect to the fluid,

the magnitude of the pressure gradient the magnitude of the pressure gradient between the front and rear ends of the body,between the front and rear ends of the body,


Form dragForm drag

and the size of the surface area that is and the size of the surface area that is aligned perpendicular to the flow.aligned perpendicular to the flow.

Streamlining helps to minimize form drag.Streamlining helps to minimize form drag.


Wave dragWave drag

Resistance created by the generation of Resistance created by the generation of waves at the interface between two different waves at the interface between two different fluids, such as air and water.fluids, such as air and water.


Wave dragWave drag

Although bodies that are completely Although bodies that are completely submerged in a fluid are not affected by submerged in a fluid are not affected by wave drag, this form of drag can be a major wave drag, this form of drag can be a major contributor to the overall drag acting on a contributor to the overall drag acting on a human swimmer, particularly when the human swimmer, particularly when the swim is done in open water.swim is done in open water.


Wave dragWave drag

When a swimmer moves a body segment When a swimmer moves a body segment along, near, or across the air and water along, near, or across the air and water interface, a wave is created in the more interface, a wave is created in the more dense fluid (the water).dense fluid (the water).

The reaction force the water exerts on the The reaction force the water exerts on the swimmer constitutes wave drag.swimmer constitutes wave drag.


Wave dragWave drag

At fast swimming speeds, wave drag is At fast swimming speeds, wave drag is generally the largest component of the total generally the largest component of the total drag acting on the swimmer.drag acting on the swimmer.


Lift ForceLift Force

Force acting on a body in a fluid in a Force acting on a body in a fluid in a direction perpendicular to the fluid flow.direction perpendicular to the fluid flow.


Coefficient of LiftCoefficient of Lift

Unitless number that is an index of a body’s Unitless number that is an index of a body’s ability to generate lift.ability to generate lift.


FoilFoil

Shape capable of generating lift in the Shape capable of generating lift in the presence of a fluid flow.presence of a fluid flow.


Bernoulli’s PrincipleBernoulli’s Principle

An expression of the inverse relationship An expression of the inverse relationship between relative velocity and relative between relative velocity and relative pressure in a fluid flow.pressure in a fluid flow.



According to this principle, regions of According to this principle, regions of relative high velocity fluid flow are relative high velocity fluid flow are associated with regions of relative low associated with regions of relative low pressure, and regions of relative low pressure, and regions of relative low velocity are associated with regions of velocity are associated with regions of relative high pressure.relative high pressure.



When these regions of relative low and high When these regions of relative low and high pressure are created on opposite sides of the pressure are created on opposite sides of the foil, the result is a lift force directed foil, the result is a lift force directed perpendicular to the foil from the high perpendicular to the foil from the high pressure zone toward the low pressure zone.pressure zone toward the low pressure zone.


Factors affecting lift forceFactors affecting lift force

The greater the velocity of the foil relative The greater the velocity of the foil relative to the fluid, the greater the pressure to the fluid, the greater the pressure differential and the lift force generated.differential and the lift force generated.



As fluid density increases and/or surface As fluid density increases and/or surface area increases on the flat side of the foil, lift area increases on the flat side of the foil, lift increases.increases.

The shape of the object also determine lift The shape of the object also determine lift capabilities (coefficient of lift).capabilities (coefficient of lift).


Angle of attackAngle of attack

Angle between the longitudinal axis of a Angle between the longitudinal axis of a body and the direction of the fluid flow.body and the direction of the fluid flow.

A positive angle of attack is necessary to A positive angle of attack is necessary to generate a lift force. generate a lift force.



As the angle of attack increases, the amount As the angle of attack increases, the amount of surface area exposed perpendicularly to of surface area exposed perpendicularly to the fluid also increases, thereby increasing the fluid also increases, thereby increasing the amount of form drag acting.the amount of form drag acting.



With too steep of an angle of attack, the With too steep of an angle of attack, the fluid cannot flow along the curved side of fluid cannot flow along the curved side of the foil or create.the foil or create.

This can cause a stall and loss in altitude.This can cause a stall and loss in altitude.


Lift/drag ratioLift/drag ratio

The magnitude of the lift force divided by The magnitude of the lift force divided by the magnitude of the total drag force acting the magnitude of the total drag force acting on a body at a given time.on a body at a given time.


Magnus EffectMagnus Effect

Spinning objects also generate lift.Spinning objects also generate lift. When an object in a fluid medium spins, the When an object in a fluid medium spins, the

boundary layer of fluid molecules adjacent boundary layer of fluid molecules adjacent to the object spins with it.to the object spins with it.



This creates a region of relative low This creates a region of relative low velocity and high pressure.velocity and high pressure.

On the opposite side of the spinning object, On the opposite side of the spinning object, the boundary layer moves in the same the boundary layer moves in the same direction as the fluid flow, thereby creating direction as the fluid flow, thereby creating a zone of relative high velocity and low a zone of relative high velocity and low pressure.pressure.



This pressure differential creates a lift force This pressure differential creates a lift force directed from the high pressure region to directed from the high pressure region to the low pressure region (curve ball).the low pressure region (curve ball).

Illinois State University Chapter 8 ä Fluid Mechanics ä The Effects of Water and Air.

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