chapter 3 types of flow
TRANSCRIPT
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 1/18
FLUID MECHANIC
CHE 203Chapter 3
Types of Flow
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 2/18
CHAPTER 3TYPES OF FLOW
FLUID MECHANICS (CHE 203)
3.1 FLUID FLOW
3.2 UNIFORM FLOW AND STEADY FLOW
3.3 COMPRESSIBLE AND INCOMPRESSIBLE FLOW
3.4 LAMINAR AND TURBULENT FLOW
3.5 REYNOLDS NUMBER
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 3/18
LEARNING OUTCOMES
At the end of this chapter, student should be able to:
i Define each types of flow including pathline, streamline andstream tube
ii Discuss the differences / characteristics of steady,
unsteady, uniform, non-uniform, laminar, transitional and
turbulent flow
iii Calculate Reynolds Numberiv Determine the types of flow based on Reynolds Number
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 4/18
A liquid particle
Pipe
3.1 FLUID FLOW
Pathlines : The path followed by a liquid particle in motion is called a pathline. Thus, the pathline shows the direction of a particle for a certain
period of time or between two given section.
Chapter 3
Path line
t1t0
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 5/18
3.1 FLUID FLOW
Streamlines : The imaginary line drawn in a fluid, in such a way that the
tangent to which at any point gives the direction of motion at the point. Thus,the stream line shows the direction of motion of a number of particles at the
same time.
• Because the fluid is moving in the same direction as the streamlines, fluid
can not cross a streamline.
• Streamlines can not cross each other. If they were to cross this would
indicate two different velocities at the same point. This is not physically
possible.
• The above point implies that any particles of fluid starting on one
streamline will stay on that same streamline throughout the fluid.
Streamlines around a wing shaped body
Chapter 3Example:
Video Clip
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 6/18
3.1 FLUID FLOW
Streamtube
An element of fluid, bounded by a number of streamlines, which confine theflow. As there is no movement of fluid across a streamline, therefore the fluidinside the streamtube cannot escape through its walls.
A Streamtube
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 7/18
3.2 UNIFORM FLOW AND STEADY FLOW
The following terms describe the states which are used to classify fluidflow:
1. Uniform flow: If the flow velocity is the same magnitude and
direction at every point in the fluid it is said to be uniform.
2. Non-uniform: If at a given instant, the velocity is not the same at
every point the flow is non-uniform. (In practice, by this definition,every fluid that flows near a solid boundary will be non-uniform - as
the fluid at the boundary must take the speed of the boundary,
usually zero. However if the size and shape of the of the cross-
section of the stream of fluid is constant the flow is considered
uniform.)
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 8/18
3.2 UNIFORM FLOW AND STEADY FLOW
3. Steady:
A steady flow is one in which the conditions (velocity, pressure and cross-section) may differ from point to point but DO
NOT change with time.
4. Unsteady: If at any point in the fluid, the conditions change with
time, the flow is described as unsteady. (In practice there is always
slight variations in velocity and pressure, but if the average values
are constant, the flow is considered steady).
Chapter 3
Example: Video Clip
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 9/18
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 10/18
• All fluids are compressible - even water - their density will change as
pressure changes.• But under steady flow conditions, and provided that the changes in pressure
are small, it is usually possible to simplify analysis of the flow by assuming
it is incompressible and has constant density.
• Since liquids are quite difficult to compress - so under most steady
conditions they are treated as incompressible.
• In some unsteady conditions, very high pressure differences can occur and
it is necessary to take these into account - even for liquids.
• Gasses are easily compressed, it is essential in most cases to treat these as
compressible, taking changes in pressure into account.
3.3 COMPRESSIBLE AND INCOMPRESSIBLE FLOW
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 11/18
3.4 LAMINAR AND TURBULENT FLOW
The left situation is known as laminar flow and the right as turbulent flow.
Solution is introduced from the right handside and pumped through the pipe. If
the flow is controlled, after a small lead in length, the profile will become stable
with no mixing in the lateral direction, this is termed Laminar flow.
If however the solution is pumped through the cell at a high rate then the
transport can become Turbulent, where the solution movement is essentially arandom and unpredictable.
The laminar flow occurs when the fluid is flowing slow and the turbulent flow
occurs when it is flowing fast.
Laminar flow Turbulent flow
Chapter 3
Example: Video Clip
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 12/18
Laminar Turbulent
Re < 2000 Re > 4000
'low' velocity 'high' velocity
Dye does not mix with water Dye mixes rapidly and completely
Fluid particles move in straight lines Particle paths completely irregular
Simple mathematical analysis possible Average motion is in the direction ofthe flow
Rare in practice in water systems Cannot be seen by the naked eye
Changes/fluctuations are very difficult
to detect. Must use laser
Mathematical analysis very difficult -so experimental measures are used
Most common type of flow.
3.4 LAMINAR AND TURBULENT FLOW
Chapter 3
Example: Video Clip
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 13/18
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 14/18
But what is fast or slow? And at what
speed does the flow pattern change? Andwhy might we want to know this?
In order to predict this change over
between turbulent and laminar behaviour,
work was carried out by Hagan in the mid1840's and later by Reynolds who was the
first to put forward a predictive model. In
this particular example there is a maximum
velocity in the centre and minimum
velocity at the side walls.
A tank is arranged with a pipe taking water
from the centre into which a dye is injected
through a needle.
Reynold’s Experiment
Storage
tank
Collection
tank
Dye
3.5 REYNOLDS NUMBER
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 15/18
After many experiments by Reynolds, he found that the expression belowwould help to predict the change in flow type.
3.5 REYNOLDS NUMBER
ud
This value is known as the Reynolds number, Re:
udRe
If the value is less than about 2000 then flow is laminar, if greater than 4000
then turbulent and in between these then in the transition zone.
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 16/18
Laminar flow : Re < 2000
Transitional flow : 2000 < Re < 4000Turbulent flow : Re > 4000
What are the units of this Reynolds number? We can fill in the equation with SI unit
1kg
ms
1
m
s
m
m
kgudRe
ms/kgm/ Nsmd
s/mu
m/kg
3
2
3
It has no units. A quantity that has no units is known as a non-dimensional
(or dimensionless) quantity.
Thus the Reynolds number, Re is a non-dimensional number.
3.4 REYNOLDS NUMBER
Chapter 3
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 17/18
EXAMPLE
If the pipe and the fluid have the following properties:
Water density, ρ = 1000 kg/m3
Pipe diameter, d = 0.5m
Dynamic viscosity, μ = 0.55 x 10-3 Ns/m2
What is the maximum velocity when the Re is 2000.
Chapter 3
Answer
8/12/2019 Chapter 3 Types of Flow
http://slidepdf.com/reader/full/chapter-3-types-of-flow 18/18
If this were a pipe in a house central heating system, where the pipe diameter
is typically 0.015m, what is the limiting velocity for laminar flow would be?
Chapter 3
Answer