3. Fluid in Motion
FLUID MECHANICS deals with the
behaviour of fluids
at rest or
in motion,
and
the interaction of fluids with
solids or
other fluids at the boundaries.
Wide variety of fluid flow problems
convenient to classify them on the basis of some common
characteristics 3
6. There is no fluid with zero viscosity, and thus all fluid flows involve viscous
effects to some degree.
Viscous versus Inviscid Regions of Flow
Viscous Flows :
Flows in which the frictional effects are significant.
However,
in practical interest, there are regions (typically regions not close to solid
surfaces) where viscous forces are negligibly small compared to inertial
or pressure forces.
Inviscid Flow Regions
The flow of an
originally uniform
fluid stream over a
flat plate,
Depending on whether the viscous
effect is considerable or not
6
7. Internal versus External Flow
External Flow :
The flow of an unbounded fluid over a surface such as
a plate, a wire, or a pipe.
Internal flow :
When the fluid is completely bounded by solid
surfaces, then the flow is termed as internal.(The flow
in a pipe or duct )
Internal flows are dominated by the influence of viscosity throughout
the flow field.
External flows :the viscous effects are limited to boundary layers near
solid surfaces and to wake regions downstream of bodies.
Depending on whether the fluid is forced to
flow in a confined channel or over a surface
7
8. Compressible versus Incompressible Flow
Depending on the level of variation
of density during flow.
Incompressible Flow:
If the density remains nearly constant throughout fluid flow.
The densities of liquids are essentially constant
liquids are usually referred to as incompressible
substances
Gases, on the other hand, are highly compressible.
Mach number ,
Gas flows can often be approximated as incompressible if
Speed of Sound = 346 m/s (in air at room temp at sea
level)
Ma = 1:Sonic Flow, Ma <1: Subsonic Flow,
Ma>1:Supersonic Flow, Ma>>1:Hypersonic Flow
8
9. Laminar versus Turbulent Flow
Depending on whether flows are
smooth or rather chaotic
Laminar Flow:
The highly ordered fluid motion characterized by
smooth layers of fluid.
The flow of high-viscosity fluids such as oils at low
velocities is typically laminar
Turbulent Flow
The highly disordered fluid motion that typically
occurs at high velocities and is characterized by
velocity fluctuations.
The flow of low-viscosity fluids such as air at high
velocities is typically turbulent
A flow that alternates between being laminar and
turbulent is called Transitional. 9
10. Steady versus Unsteady Flow
Depending on whether flows are
change over the time or not
Steady no change at a point with time
Unsteady change at a point with time
Steady-Flow Devices
Devices that operate for long periods of time under the same
conditions
EX: turbines, compressors, boilers, condensers, and heat exchangers
Some cyclic devices, such as reciprocating engines or compressors, do
not satisfy the steady-flow conditions since the flow at the inlets and
the exits is pulsating and not steady.
10
11. One, Two, and Three-Dimensional Flows
Depending on whether the flow velocity varies
in one, two, or three primary dimensions,
respectively
The development of the velocity profile in a circular pipe. V = V(r, z)
and thus the flow is two-dimensional
Flow over a car antenna is
approximately two-
dimensional
11
12. Natural (or Unforced) versus Forced Flow
Depending on how the fluid motion is initiated
(i.e. by forced or naturally)
Forced Flow:
A fluid is forced to flow over a surface or in a pipe by
external means such as a pump or a fan.
Natural Flows:
Any fluid motion is due to natural means such as the
buoyancy effect.
12
13. The subject called kinematics concerns the study of motion.
In fluid dynamics, fluid kinematics is the study of how fluids flow and how
to describe fluid motion.
Lagrangian and Eulerian
Descriptions
Fundamentally, there are two distinct ways to describe motion.
1.Lagrangian description
The kinematics of experiments which involves keeping track of the
position vector of each object and the velocity vector of each object as
functions of time. When this method is applied to a flowing fluid, we
call it the Lagrangian description of fluid motion.
Newton’s laws are used to describe the motion of such objects.
With a small number of objects, such as billiard balls on a pool
table, individual objects can be tracked.
This method of describing motion is much more
difficult for fluids than for billiard balls!
[By Italian mathematician Joseph Louis Lagrange (1736–1813)]
13
14. Lagrangian and Eulerian
Descriptions
2.Eulerian description
[Swiss mathematician Leonhard Euler (1707–1783)]
A finite volume called a flow domain or control volume, through which
fluidflows in and out is defined
Do not need to keep track of the position and velocity of a mass of fluid particles
of fixed identity
Define field variables, functions of space and time, within the control volume
Examples:
Pressure field:
For general unsteady three dimensional fluid flow in Cartesian coordinates
Velocity field:
scalar field vector field 14
15. Flow Visualization - Fundamental
Gives “whole picture” rather than merely a list of numbers and quantitative
data
Useful not only in physical experiments but in numerical solutions as well
[computational fluid dynamics (CFD)].
Streamlines and Streamtubes
Pathlines
Streaklines
Timelines
Flow patterns that can be visualized
15
16. Streamlines and Stream-tubes
A streamline is a curve that is every where
tangent to the instantaneous local velocity
vector.
Streamlines are useful as indicators of the instantaneous
direction of fluid motion throughout the flow field.
A streamtube consists of a bundle of streamlines
Since streamlines are everywhere parallel to the local
velocity, fluid cannot cross a
streamline by definition.
16
17. Pathlines
A pathline is the actual path traveled by an individual fluid particle
over some time period.
A pathline is the same as the fluid
particle’s material position vector
(x(t), y(t), z(t)),
17
18. Streaklines
A streakline is the locus of fluid particles that have passed sequentially through a
prescribed point in the flow.
If you insert a small tube into a flow and
introduce a continuous stream of tracer fluid
(dye in a water flow or smoke in an airflow),
the observed pattern is a streakline.
18
19. A timeline is a set of adjacent fluid particles that were
marked at the same (earlier) instant in time.
Timeline
Timelines are particularly
useful in situations where
the uniformity of a
flow (or lack thereof) is to
be examined.
Timelines are formed by marking a line of fluid particles, and then
watching that line move (and deform) through the flow field
19
22. Continuity of Flow
For steady
flow,
ui = velocities measured at right
angles to the cross sectional area δAi
ρi = density of fluid at cross-section i
EQUATION OF CONTINUITY
22
23. Equation of Continuity –
For Steady Flow
If the fluid is incompressible,
incompressible,
flow towards the junction as positive
flow away from the junction as negative,
For steady flow,
If ,
23
24. Example 1
Water flows from A to D and E through the series pipeline is shown in figure. Given
the pipe diameters, velocities and flow rates below, complete the missing data for
this system.
24
30. Continuity Equation
For Two –Dimensional incompressible flow
Cartesian Coordinates
Cylindrical Coordinates
30
31. Example
The velocity distribution for the flow of an
incompressible fluid is given by
vx = 3 - x,
vy = 4 + 2y,
vz = 2 - z.
Show that this satisfies the requirements of the
continuity equation.
Continuity Equation
For Two –Dimensional incompressible flow
31
![ The subject called kinematics concerns the study of motion.
In fluid dynamics, fluid kinematics is the study of how fluids flow and how
to describe fluid motion.
Lagrangian and Eulerian
Descriptions
Fundamentally, there are two distinct ways to describe motion.
1.Lagrangian description
The kinematics of experiments which involves keeping track of the
position vector of each object and the velocity vector of each object as
functions of time. When this method is applied to a flowing fluid, we
call it the Lagrangian description of fluid motion.
Newton’s laws are used to describe the motion of such objects.
With a small number of objects, such as billiard balls on a pool
table, individual objects can be tracked.
This method of describing motion is much more
difficult for fluids than for billiard balls!
[By Italian mathematician Joseph Louis Lagrange (1736–1813)]
13](https://image.slidesharecdn.com/fluidmechanicsandhydraulicslec02fluiddynamicsomeaga-250326175213-86d18247/85/Fluid-Mechanics-and-Hydraulics_Lec-02_fluid-dynamics_Omeaga-ppt-13-320.jpg)
![Lagrangian and Eulerian
Descriptions
2.Eulerian description
[Swiss mathematician Leonhard Euler (1707–1783)]
A finite volume called a flow domain or control volume, through which
fluidflows in and out is defined
Do not need to keep track of the position and velocity of a mass of fluid particles
of fixed identity
Define field variables, functions of space and time, within the control volume
Examples:
Pressure field:
For general unsteady three dimensional fluid flow in Cartesian coordinates
Velocity field:
scalar field vector field 14](https://image.slidesharecdn.com/fluidmechanicsandhydraulicslec02fluiddynamicsomeaga-250326175213-86d18247/85/Fluid-Mechanics-and-Hydraulics_Lec-02_fluid-dynamics_Omeaga-ppt-14-320.jpg)
![Flow Visualization - Fundamental
Gives “whole picture” rather than merely a list of numbers and quantitative
data
Useful not only in physical experiments but in numerical solutions as well
[computational fluid dynamics (CFD)].
Streamlines and Streamtubes
Pathlines
Streaklines
Timelines
Flow patterns that can be visualized
15](https://image.slidesharecdn.com/fluidmechanicsandhydraulicslec02fluiddynamicsomeaga-250326175213-86d18247/85/Fluid-Mechanics-and-Hydraulics_Lec-02_fluid-dynamics_Omeaga-ppt-15-320.jpg)
