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

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
 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

continued……..
 When drag forces can’t 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
Fluid speed at surface is zero
Increasing
Speed
Frictional Drag: Drag is produced by friction between layers of fluid

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

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 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 car’s speed increases

 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

continued……..
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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
Layer of fluid of thickness
Top plate is pulled to the right at a constant speed v
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.

continued……..
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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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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:
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Proportional to A and v, and
Inversely proportional to the thickness of the fluid layer,

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

 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

 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.

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

 http://www.youtube.com/watch?v=X4zd4Qpsbs8

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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.

continued……..
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The drag force acts in the direction opposite the object’s 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 fluid’s viscosity :

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

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?

 http://www.youtube.com/watch?v=1ukf2vntU44

 Poiseuille’s law gives the volume flow rate of a fluid flowing through a tube or pipe.
 Like Stokes’ law,
Poiseuille’s law applies to laminar flow.
The fluid layer at the center moves the fastest
Layers nearer the wall move more slowly
Fluid in contact with the wall does not move

continued……..
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Jean Louis Poiseuille was a physician who was also trained as a physicist and mathematician.
In the mid – 1840’s, 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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 Poiseuille’s 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

Factors Affecting Flow Through a Pipe
 Resistance decreases the flow rate V of fluid through a pipe
 Poiseuille’s law shows this resistance depends on three factors:
 1. The radius of the pipe
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2. The length of the pipe
3. The viscosity of the fluid

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.

Factors Affecting Flow Through a Pipe
 Fluid resistance decreases as pipe radius and crosssection area increase
 Larger pipe = greater volume of fluid per second
 Larger pipe also has a lower resistance to flow

Factors Affecting Flow Through a Pipe
 Longer pipes have higher fluid resistance
Volume flow rate is inversely proportional to length
 If the length of the pipe is doubled the resistance is doubled and the volume flow is halved.

Factors Affecting Flow Through a Pipe
 Volume flow rate is inversely proportional to viscosity.
 If you use a fluid with half the viscosity, you double the volume flow rate

Factors Affecting Flow Through a Pipe continued…
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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

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

 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

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