This document provides an introduction to key concepts in fluid mechanics. It defines fluids as substances that flow and take the shape of their container. When at rest, this is called fluid statics, and when in motion it is called fluid dynamics. Key concepts discussed include: pressure, which increases with depth in static fluids; density; viscosity, which provides resistance to flow; laminar and turbulent flow; the equation of continuity, which states that mass flow rate remains constant; and Bernoulli's equation, which relates pressure and speed such that increased speed means decreased pressure.
2. Outline
• What is a fluid?
• Some concept related to the fluid
– Pressure
– Density
• fluid Mechanism
– Fluid in motion
• Flow Rate and viscosity
• the Equation of Continuity
• Bernoulli’s Equation
3. Fluids
Liquids and gases are both fluids:
a fluid is any substance that flows and takes the shape of its
container.
If the fluids are at rest, the study of them is called fluid statics.
If the fluids are in motion, the study of them is called fluid
dynamics.
http://physics.bu.edu/~duffy/py105.html
4. Definition of a Fluid
A fluid is a substance that flows under the action of shearing
forces. If a fluid is at rest, we know that the forces on it are in
balance.
A gas is a fluid that is easily compressed. It fills any vessel in
which it is contained.
A liquid is a fluid which is hard to compress. A given mass of
liquid will occupy a fixed volume, irrespective of the size of
the container.
5. Fluids can be compressible or incompressible.
This is the big difference between liquids and gases,
because liquids are generally incompressible, meaning
that they don't change volume much in response to a
pressure change; gases are compressible, and will
change volume in response to a change in pressure.
6. Density
The density (or mass density) of a fluid is defined as
its mass per unit volume. It is denoted by the Greek
symbol, .
=
V m3
kgm-3
water= 998 kgm-3
air =1.2kgm-3
kg
m
• Water, for example, has a density of about 1 gram per milliliter. (It
varies slightly with temperature and pressure.)
• In general, liquids and solids have similar densities, which are of the
order of 1000 kg / m3. Gases, on the other hand, have densities around
1 kg / m3
7. Pressure
Pressure is the force per unit area, where the force is
perpendicular to the area.
p=
A m2
Nm-2
(Pa)
N
F
The SI unit for pressure is the Pascal (Pa), equal to
one newton per square metre.
The Absolute pressure, is the pressure compared with a
pressure at vacuum (zero space).
pa= 105 Nm-2
1psi =6895Pa
8. 8
The pressure is the same in every
direction in a fluid at a given depth.
Pressure in a fluid acts equally in
all directions
Pressure
9. Pressure
Pressure in a static liquid increases
linearly with depth
p=
increase in
depth (m)
pressure
increase
g h
Pressure varies with depth.
Pressure vs. depth in a static fluid
10. Pressure/Density Example
Tofu
Cookbook
To calculate the pressure on the table, it depends on the book’s orientation.
The book’s density is 6 lb/(9”·14”·3”) = 0.0159 lb/in3.
P α 1/A
Tofu Cookbook
14”
3”
9”
P=F/A
P = 6 lb/(9”·14”)
= 0.0476 lb/in2
P = 6 lb/(9”·3”)
= 0.222 lb/in2
P = 6 lb/(3”·14”)
= 0.143 lb/in2
11. Fluid dynamics
• Fluid dynamics is the study of how fluids behave when they're
in motion.
• Fluids can flow steadily, or be turbulent.
• In steady flow, the fluid passing a given point maintains a
steady velocity. If the flow of a fluid is smooth, it is called
streamline or laminar flow (a).
http://www.youtube.com/watch?v=OW5wB8rJ8Zc
http://www.nano-lane.com/resource-center/videos/
12. 12
Fluid dynamics
• Above a certain speed, the flow becomes turbulent (b).
• For turbulent flow, the speed and or the direction of the flow
varies. In steady flow, the motion can be represented with
streamlines showing the direction the water flows in different
areas
.
http://www.youtube.com/watch?v=yOU9BvyKpi8&feature=youtu.be
13. Reynolds classified the flow type according to the motion of the fluid.
Laminar Flow: every fluid
molecule followed a straight path
that was parallel to the
boundaries of the tube.
Turbulent Flow: every fluid
molecule followed very complex
path that led to a mixing of the
dye.
Transitional Flow: every fluid
molecule followed wavy but
parallel path that was not parallel
to the boundaries of the tube.
15. In our study of fluids, we are going to
investigate different properties.
The first one is
VISCOSITY!
What is VISCOSITY?
Viscosity is an internal property of a fluid that offers resistance to flow
16. VISCOSITY is a measure of the resistance
that a fluid has to movement and flowing.
Low viscosity = thin = low resistance to flow
High viscosity = thick = high resistance to flow
Viscosity is the property of a fluid that has
internal friction
Viscosity has units of (pressure) (time).
17. Why does VISCOSITY matter?
When a fluid is stationary, viscosity is not a
concern. However, when a fluid is flowing,
or when something is moving through a
fluid, the property of viscosity is very
important.
18. 18
Viscous Flow
(a) In ideal (nonviscous)
fluid flow, all fluid particles
across the pipe have the
same velocity.
(b) In viscous flow, the speed
of the fluid is zero at the
surface of the pipe and
increases to a maximum
along the center axis.
19. How can we compare the VISCOSITY of
different substances?
Viscosity can only be discussed when it is compared
to another substance.
One way to measure the viscosity of a liquid
quantitatively involves timing how long it takes
the liquid to flow out a funnel.
This is referred to as: FLOW RATE
20. FLOW RATE can be defined as
the time required for a specific
fluid to move.
FLOW RATE is measured in
millilitres per second (ml / sec)
21. 21
We will deal with laminar flow.
The equation of continuity states that:
The mass flow rate is the mass that passes a given
point per unit time. The flow rates at any two
points must be equal, as long as no fluid is being
added or taken away.
This gives us the equation of continuity:
Equation of Continuity
22. 22
The Equation of Continuity
Equation of continuity: If a fluid
enters one end of a pipe at a
certain rate (e.g., 5 kilograms per
second), then fluid must also leave
at the same rate, assuming that
there are no places between the
entry and exit points to add or
remove fluid.
The mass of fluid per second (e.g.,
5 kg/s) that flows through a tube is
called the mass flow rate.
24. 24
EQUATION OF CONTINUITY
The mass flow rate ( Av) has the same value at every
position along a tube that has a single entry and a single
exit point for fluid flow. For two positions along such a
tube
= fluid density (kg/m3)
A = cross-sectional area of tube (m2)
v = fluid speed (m2)
SI Unit of Mass Flow Rate: kg/s
2
2
2
1
1
1 v
A
v
A
26. 26
Flow Rate and the Equation of Continuity
mass flowing in = mass flowing out
------------------------------------------
------------------------------------------
If the density doesn’t change – typical for liquids – this
simplifies to:
27. • Making fluids flow
There are basically two ways to make fluid flow through a pipe.
One way
is to make the pressure at one end of the pipe larger than the
pressure at the other end. A pressure difference is like a net force,
producing acceleration of the fluid.
The second way
is to tilt the pipe so the flow is downhill, in which case
gravitational kinetic energy is transformed to kinetic energy.
28. 28
Bernoulli’s Equation
A fluid can also change its
height. By looking at the
work done as it moves, we
find:
This is Bernoulli’s equation. One
thing it tells us is that as the speed
goes up, the pressure goes down
29. In summary
• Pressure, density and viscosity
• Static and dynamic fluid
• Equation of Continuity
• Bernoulli’s Equation
• Application and example
