Resistance In Fluid Systems

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Resistance In Fluid Systems

• Principles of Technology

All content was received from Physics In Context
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Drag

• When one solid object slides against another, a
  force of friction opposes the motion
• When a solid object moves through a fluid, there
  is also a force that opposes the motion.

• Examples
• Boat moves through water
• Airplane moves through air
• You can feel drag when you stand in high wind
• Or when you put your hand out the window of a
  moving car

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Laminar Turbulent Flow

• These factors make it difficult to calculate drag
  exactly.
• You can Approximate
• Simplest approximation is to ignore drag forces
  when they are small
• Example
• Ignore drag for an object moving slowly in fluids
  such as air or water
• Although very slow speeds
• produce significant drag in fluids such as motor
  oil

• The Drag exerted on an object by fluid depends on
  many factors
• Speed of the object (or fluid)
• Size and shape of the object
• Physical properties of the fluid

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Laminar Turbulent Flow continued..

• When drag forces cant be ignored, you can make
  two approximations about the fluid the flow can
  be Laminar or Turbulent.

Streamline
Laminar (streamlined flow) is a slow, smooth
flow over a surface, in which the paths of
individual particles do not cross
Increasing Speed
Fluid speed at surface is zero
Frictional Drag Drag is produced by friction
between layers of fluid
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Laminar Turbulent Flow continued..

• Turbulence produces the visible wake behind a
  moving boat and an invisible wake behind a moving
  plane or car.

• Turbulent Flow
• Is irregular flow with eddies and whorls causing
  fluid to move different directions
• Turbulence is produced by high speeds, by shapes
  that are not streamlined, and by sharp bends in
  the path of a fluid

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Laminar Turbulent Flow continued..

• Changing the direction of the fluid into eddies
  and whorls requires work.
• When Fluid does work, the pressure drops.
• Thus, the fluid pressure in the wake is less than
  the fluid pressure in the streamlined flow.

• Pressure Drag This pressure difference causes a
  force to act on the object in the direction
  opposite its relative velocity.

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Frictional Pressure Drag

• Frictional drag and pressure drag both increase
  as speed increases
• Low speeds, the drag forces on the car is
  frictional drag
• The force increases linearly with speed
• (Doubling speed Doubling frictional force)
• Higher speeds, turbulence and pressure drag are
  more and more important.
• This force increases as the square of the speed
• Doubling the speed increases the pressure drag by
  a factor of four

The drag force on a car increases as the cars
speed increases
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Viscosity

• Friction between two solid surfaces cause a
  resistance to movement between the surfaces
• Viscosity is the property of a fluid that has
  internal friction
• We use the Greek letter
• (eta) to represent viscosity

• Example
• Bubble gum has a high viscosities
• Air water have a much lower viscosities

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Viscosity continued..

• The fluid in contact with the top plate moves
  with the plate at speed v, and the fluid in
  contact with the bottom plate remains motionless.
• The speed of the fluid between the top and bottom
  varies linearly.
• The top plate drags layers of fluid with it.
• The force F is required to overcome the
  resistance and keep the plate moving at constant
  speed

Top plate is pulled to the right at a constant
speed v
Layer of fluid of thickness
Bottom plate held in place
The viscosity of a fluid can be measured by
pulling a plate at constant speed across a layer
of the fluid.
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Viscosity continued..

• As long as the plate speed v is not so large that
  turbulence occurs, the fluid flow between the
  plates is laminar.
• The force F required to maintain a constant speed
  for most fluids in laminar flow is found to be
• Proportional to A and v, and
• Inversely proportional to the thickness of the
  fluid layer,

• When the plate moves to the right at constant
  speed, no net force is acting on the plate.
• Therefore, the fluid exerts a force of friction,
  or drag force F drag on the plate to the left,
  opposing motion. The magnitude of the drag force
  equals F.

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Viscosity continued..

• The proportionality constant is the viscosity of
  the fluid.
• Viscosity has units of (pressure) (time).
• The SI units for viscosity are or
• The English units are or

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Viscosities of Common Fluids

• Viscosity of most liquids decreases as
  temperature increases.
• Viscosity of most gases increase with temperature
• Example
• Cold honey is thick with a high viscosity
• Hot honey is watery with a low viscosity

• Pg. 188 Chapter 4

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Motor Oil Viscosity

• SAE Society of Automotive Engineers
• 10W The viscosity of the oil when measured at 0
  degrees F (the W means winter grade)
• 30 The viscosity of the oil when measured at
  212 degrees F.

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Motor Oil Viscosity continued..
These oils were chilled to -35 degrees C for 16
hours. The photo was taken 30 seconds after the
caps were removed from the containers.

• SAE Viscosity recommendations for various climates

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Viscosity Cool Science Trick

• http//www.youtube.com/watch?vX4zd4Qpsbs8

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Stokes Law

• IN 1845, the Irish mathematician and physicist
  George Stokes used viscosity and the equations of
  fluid flow to predict the drag force on a sphere
  moving through a fluid.
• It applies to objects moving at low enough speeds
  that the flow of fluids around the objects is
  streamlined, or laminar.
• In these cases, there is no turbulence and the
  only drag force on the objects is due to
  frictional drag.

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Stokes Law continued..

• The drag force acts in the direction opposite the
  objects velocity (it opposes motion).
• The drag force equals the product of a constant
  (6 for a sphere), the radius r of the object,
  the speed v of the object (or the relative speed
  between the object and fluid), and the fluids
  viscosity

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Terminal Speed

• When an object moves through a fluid, the drag
  force on the object increases as the speed
  increases.

• Drop a baseball from a high tower at first it
  has a low speed and a low drag
• The force of gravity acting downward is greater
  then the drag force acting upward.
• Therefore, a net force acts downward on the
  baseball and it accelerates downward.
• As the speed increases the drag increases, until
  the upward drag the weight.
• At this point the forces are balanced and no
  longer accelerates.

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

• The terminal speed of a baseball is about 40
  m/s, but the terminal speed of a basketball is
  only about 20 m/s.
• Which ball has a greater drag force at any given
  speed?

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Skydiver VS. Peregrine Falcon

• http//www.youtube.com/watch?v1ukf2vntU44

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Poiseuilles Law

• Poiseuilles law gives the volume flow rate of a
  fluid flowing through a tube or pipe.
• Like Stokes law, Poiseuilles law applies to
  laminar flow.

Layers nearer the wall move more slowly
Fluid in contact with the wall does not move
The fluid layer at the center moves the fastest
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Poiseuilles Law continued..

• Jean Louis Poiseuille was a physician who was
  also trained as a physicist and mathematician.
• In the mid 1840s, he experimented with water
  flowing through glass capillary tubes as a
  simulation of blood flowing through small blood
  vessels.
• Poiseuille learned that the rate at which fluid
  flows through a tube increases proportionately to
  the pressure applied and to the fourth power of
  the radius of the tube

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Poiseuilles Law continued..

• Poiseuilles law the volume flow rate
  of a fluid of viscosity through a tube
  or pipe of radius r and length L is

• The internal friction of the fluid causes the
  pressure to decrease as the fluid flows.

the change in pressure of the fluid as it flows
the length L
Is negative therefore V is positive
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Factors Affecting Flow Through a Pipe

• Resistance decreases the flow rate V of fluid
  through a pipe
• Poiseuilles law shows this resistance depends on
  three factors
• 1. The radius of the pipe
• 2. The length of the pipe
• 3. The viscosity of the fluid

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Factors Affecting Flow Through a Pipe continued

• The 3 factors of resistance can be illustrated
  using graphs of volume flow rate versus pressure
  drop.
• Fluid resistance R as the ratio of the prime
  mover to the volume flow rate.
• The prime mover in fluid systems as pressure
  change, or pressure drop.
• Pressure drop is
• is negative, so pressure drop and fluid
  resistance are positive.

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Factors Affecting Flow Through a Pipe Dependence
on Radius

• Fluid resistance decreases as pipe radius and
  cross-section area increase
• Larger pipe greater volume of fluid per second
• Larger pipe also has a lower resistance to flow

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Factors Affecting Flow Through a Pipe Dependence
on Length

• Longer pipes have higher fluid resistance
• If the length of the pipe is doubled the
  resistance is doubled and the volume flow is
  halved.

Volume flow rate is inversely proportional to
length
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Factors Affecting Flow Through a Pipe Dependence
on Radius

• Volume flow rate is inversely proportional to
  viscosity.
• If you use a fluid with half the viscosity, you
  double the volume flow rate

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Factors Affecting Flow Through a Pipe continued

• If the flow becomes turbulent, resistance
  increases rapidly
• Bends and Ts in a pipe or air duct cause
  turbulence.
• When it is important to maintain laminar flow and
  reduce resistance, designers use curves with
  radii as large as possible rather than abrupt
  changes in the path of a fluid

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Factors Affecting Flow Through a Pipe continued

• Obstructions or restrictions also cause
  turbulence.
• Example
• The grill of a car is an obstruction that causes
  turbulence, affecting the aerodynamic drag of an
  automobile.
• Filters in air ducts are restrictions

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In Class Work

• Starting on page 196 in your text book
• Get into groups of 3 -4 people
• Work on the EVEN problems in groups
• If you finish team up with another group and
  compare answers
• Show work

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Homework

• Finish EVEN problems
• Move onto odd problems
• Due April 15, 2008
• At the beginning of class
• Problems 1-15 (show work)