Fundamentals of Fluid Flow
Fundamentals of Fluid Flow
Fundamentals of Fluid Flow
Introduction
Introduction
s
V Lt
t 0 t
V ui vj wk
Velocity components are in general function of x, y, z and t.
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interval.
When t is constant then it represents velocity at different
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Steady flow:
When the fluid properties like velocity, pressure, density
etc., which describe the fluid behaviour at a point, doesnt
0, 0, in general
0
t
t
t
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Unsteady flow:
When the fluid properties like velocity, pressure, density
etc., which describe the fluid behaviour at a point, change
0, 0, in general
0
t
t
t
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Uniform flow:
When the fluid velocity either in magnitude or in direction,
u
v
V
0, 0, in general
0
x
y
S
Non-Uniform flow:
When the fluid velocity changes with respect to position at a
u
v
V
0, 0, in general
0
x
y
S
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Note:
All the flows can exist independent of each other, so that
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12
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Rotational flow:
Fluid particles rotate about their mass centres while they are
moving.
Hence they will have some angular velocity,
Irrotational flow:
Fluid particles do not rotate about their mass centres while
they are moving.
Hence they will not have any angular velocity,
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Laminar flow:
Fluid particles move in layers with one layer of fluid sliding
smoothly over the adjacent layer.
Flow of viscous fluid is an example of laminar flow.
Turbulent flow:
Fluid particles move in an entirely disorderly manner, that results
in rapid and continuous mixing of fluid leading to momentum
transfer across the flow.
Flow in natural steams, artificial channels, water supply pipes etc.,
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Steam lines:
It is an imaginary line drawn in the flow field such that its tangent
at a point will gives us velocity of fluid at that point.
The pattern of fluid flow is represented by a series of steam lines.
The differential equation for a steam line in multi dimensional
coordinates is,
x y z
u
v
w
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Steam lines:
Across a steam line there can be no fluid flow.
For steady flow, steam line pattern doesnt change with respect to
time.
For unsteady flow, steam line pattern changes with respect to time.
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Steam tubes:
It is an imaginary tube formed by a group of steam lines passing
through a small closed curve, which may or may not be circular.
There will not be any flow across the boundary of stream tube.
Fluid will enter or leave the steam tube through its ends only.
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Path Lines:
It is a line traced by a single fluid particle as it moves over a
period of time.
It indicates the direction of velocity of fluid particle at successive
instant of time.
In steady flow the path line and steam lines are identical.
In unsteady flow both are different.
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Streak Lines:
It is a line traced by a fluid particles having same velocity between
different path lines at the instant of time.
In steady flow streak line, path line and steam lines are identical.
In unsteady flow they are different.
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Bank Account
Money In
Balance
Money Out
Interest
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Statement of conservation
Change in
Money
Transfer
Control
Volume
General
Quantity In
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Quantity
Generation
General
Quantity Out
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mechanics
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Eulerian description
System at t + t
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II
III
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N t t N II t t N III t t
System at t
System at t + t
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II
III
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sys
N t t Nt N II t t N II t N III t t N I t
t
t
t
t
N III t t
t
N I t
t
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dN
dt
sys
N t t N t N
Lt
t 0
t
t
CV
Rate of
Out
flow-In
flow
nV dA
dA
CS
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dN
dt
sys
CV
nV dA
CS
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Conservation of Mass
Here we consider, N = m, n = 1
dm
m
V dA
dt sys t CV CS
Assumptions:
A non deformable control volume {volume f (t)}
Control volume to be stationary {rel. vel. = abs vel.}
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Conservation of Mass
The earlier expression changes to
0 dV V dA
t CV
CS
CV t dV CS V . dA 0
V . dA . V dV
CS
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CV
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Conservation of Mass
The earlier expression changes to
CV t dV CV . V dV 0
V
CV t
dV 0
. V 0
t
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Conservation of Mass
Finally we tried to convert integral form of conservation
of mass into differential form
. V 0
t
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Exercise 01
u 3x 2 x 2 y y 3
Determine the component of the velocity along the y-
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Exercise 02
u x 2 y 2 , v y 2 z 2 , w 2 x y z
State the whether flow is continuous or not.
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Exercise 03
u x 2 2 z 2 8, v 2 y 2 z 2 6
Find the velocity component in z direction if it
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Exercise 04
u 6 xy, v 3x 2 3 y 2
Also find whether the flow is irrotational or not?
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Exercise 05
u ax 2 bxy cy 2
Find the y velocity component of fluid flow with a
condition u = 0 at y = 0. Assume that the continuity is
satisfied.
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