Chapter 4.2 Chapter 4.2 NotesNotes

Resistance in FluidsResistance in Fluids

When one solid object slides When one solid object slides against another, a force of against another, a force of frictionfriction opposes the motion. opposes the motion.

When a solid object moves When a solid object moves through a fluid, there is a also through a fluid, there is a also a force that opposes the a force that opposes the motion. This is called motion. This is called dragdrag. . Examples: boat, airplaneExamples: boat, airplane

The drag exerted on an object by The drag exerted on an object by a fluid depends on these factors:a fluid depends on these factors:

Speed of the object and fluidSpeed of the object and fluidThe size and shape of the The size and shape of the

objectobjectThe physical properties of the The physical properties of the

fluid (density)fluid (density)

The flow of a fluid can The flow of a fluid can be either be either laminarlaminar or or turbulentturbulent..

Laminar or Streamlined FlowLaminar or Streamlined Flow is a is a slow, smooth flow over a surface in slow, smooth flow over a surface in which paths of individual particles do which paths of individual particles do not cross.not cross.

The fluid speed at the surface is The fluid speed at the surface is 00 and and increases speed farther from the increases speed farther from the surface.surface.

Drag is produced by the friction Drag is produced by the friction between successive layers of fluid. between successive layers of fluid. This is called This is called frictional dragfrictional drag..

Turbulent flowTurbulent flow is irregular flow with is irregular flow with eddies and whorls causing fluid to eddies and whorls causing fluid to move in different directions.move in different directions.

Turbulence is created by Turbulence is created by high speedshigh speeds, , irregular shapesirregular shapes, and , and sharp bendssharp bends in in the path of fluid.the path of fluid.

Turbulence produces the visible wake Turbulence produces the visible wake behind moving behind moving boatsboats and the invisible and the invisible wake behind a moving wake behind a moving airplane or airplane or carcar..

The fluid pressure in the wake is The fluid pressure in the wake is lessless than the fluid pressure in the flow.than the fluid pressure in the flow.

The lower pressure in the wake causes The lower pressure in the wake causes a force to act on the object (boat or a force to act on the object (boat or car) in the opposite direction to its car) in the opposite direction to its velocity. This pressure difference in a velocity. This pressure difference in a wake is called wake is called pressure dragpressure drag..

Frictional drag and pressure drag both Frictional drag and pressure drag both increaseincrease as speed increases. as speed increases.

On a microscopic level, friction is On a microscopic level, friction is due to electrical forces between due to electrical forces between atomsatoms..

These forces create internal These forces create internal friction in the fluid, which causes a friction in the fluid, which causes a resistance to resistance to movementmovement..

ViscosityViscosity is the property of fluid is the property of fluid that describes the internal friction.that describes the internal friction.

Force = Force = viscosity (viscosity (Area x velocityArea x velocity))

thicknessthicknessF = Vis (F = Vis (A x vA x v))

yy

Viscosity DemoViscosity Demo

Viscosity of most liquids Viscosity of most liquids decreasedecrease with temperature.with temperature.

Example: cold honey is Example: cold honey is thickthick while heated honey becomes while heated honey becomes waterywatery..

As temperature increases, the As temperature increases, the molecules in the honey become less molecules in the honey become less and less tightly and less tightly boundbound to each to each other.other.

On the other hand, Viscosity of On the other hand, Viscosity of most gases most gases increasesincreases with with temperature. temperature.

Forces between gas molecules Forces between gas molecules are exerted during collisions are exerted during collisions and when heated, there are and when heated, there are more more collisionscollisions..

Stokes used Stokes used viscosityviscosity to predict to predict the drag force on a sphere the drag force on a sphere moving through a fluid when moving through a fluid when there was not turbulence.there was not turbulence.

According to According to Stoke’s LawStoke’s Law, the , the drag force is equal to the product drag force is equal to the product of a constant, the radius, the of a constant, the radius, the speed, and the viscosity.speed, and the viscosity.

Force = Force = 6 x pi x 6 x pi x radius x velocity x radius x velocity x viscosityviscosity (Stoke’s (Stoke’s Law)Law)

F = F = 6 r v 6 r v ππ visvis

What force is needed to move a What force is needed to move a sphere at a speed of 2 m/s through sphere at a speed of 2 m/s through blood if the sphere has a diameter of blood if the sphere has a diameter of 1 meter. Next through lava.1 meter. Next through lava.

Viscosity ; page 188Viscosity ; page 188 r = d/2 = 1/2 = .5r = d/2 = 1/2 = .5 F = 6 r v F = 6 r v ππ visvis F = 6 x .5 x 2 x 3.14 x .005 = F = 6 x .5 x 2 x 3.14 x .005 = .09.09 F = 6 x .5 x 2 x 3.14 x 1000 = F = 6 x .5 x 2 x 3.14 x 1000 = 18,84018,840

When an object moves through a fluid, the When an object moves through a fluid, the drag force on the object increases as the drag force on the object increases as the speed increases until at some point the speed increases until at some point the upward drag upward drag equalsequals the weight. the weight.

At this point, the forces acting on the At this point, the forces acting on the falling object are falling object are balancedbalanced and the object and the object no longer no longer acceleratesaccelerates; the speed becomes ; the speed becomes constant. constant.

The The terminal speedterminal speed of a falling object is of a falling object is the constant speed that occurs when the the constant speed that occurs when the drag force equals the gravitational force.drag force equals the gravitational force.

Poiseuille’s Law gives the Poiseuille’s Law gives the volume flow ratevolume flow rate of a fluid flowing through a tube or pipe.of a fluid flowing through a tube or pipe.

The fluid layer in the center moves the The fluid layer in the center moves the fastestfastest, and layers near the wall move the , and layers near the wall move the slowestslowest..

Poiseuille’s Law shows how resistance of a Poiseuille’s Law shows how resistance of a fluid in a pipe depends on 3 factors:fluid in a pipe depends on 3 factors:

a. Radius – larger radius = less frictiona. Radius – larger radius = less friction b. Length – shorter length = less frictionb. Length – shorter length = less friction c. Viscosity – less viscosity = less frictionc. Viscosity – less viscosity = less friction