Transcript Resistance In Fluid Systems

Resistance In Fluid Systems
Principles of Technology
All content was received from Physics In Context
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
Laminar & Turbulent Flow
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
Laminar & Turbulent Flow 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
Increasing
Speed
Fluid speed at
surface is zero
Frictional Drag: Drag is produced by friction between layers of fluid
Laminar & Turbulent Flow 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.
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.
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 car’s
speed increases
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
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.
Viscosity continued……..
 As long as the plate speed v
 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.
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,
Viscosity continued……..
 The proportionality constant is the viscosity of the
fluid.
 Viscosity has units of (pressure) (time).
 The SI units for viscosity are
 The English units are
or
or
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
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.
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
Viscosity Cool Science Trick
 http://www.youtube.com/watch?v=X4zd4Qpsbs8
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.
Stokes’ Law continued……..
 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 :
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.
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?
Skydiver VS. Peregrine Falcon
 http://www.youtube.com/watch?v=1ukf2vntU44
Poiseuille’s Law
 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.
Layers nearer
the wall move
more slowly
The fluid layer
at the center
moves the
fastest
Fluid in contact
with the wall
does not move
Poiseuille’s Law continued……..
 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
Poiseuille’s Law continued……..
 Poiseuille’s law – the volume flow rate
fluid of viscosity
and length L is:
of a
through a tube or pipe of radius r
 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
 2. The length of the pipe
 3. The viscosity of the fluid
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.
Factors Affecting Flow Through a Pipe
Dependence on Radius
 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
Dependence on Length
 Longer pipes have
higher fluid
resistance
 If the length of the
Volume flow rate is inversely proportional to
length
pipe is doubled the
resistance is
doubled and the
volume flow is
halved.
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
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
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
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
Homework
 Finish EVEN problems
 Move onto odd problems
Due: April 15, 2008
At the beginning of class
Problems 1-15 (show work)