# Conti-equation09.05

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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Lecture
9

Faculty of Engineering

Fluid Mechanics

Dr. Hasan
Hamouda

Fluid Kinematics

Fluid

kinematics

is

a

branch

of

Fluid

mechanics,

which

deals

with

the

study

of

velocity

and

acceleration

of

the

particles

of

fluids

in

motion

and

their

distribution

in

space

without

considering

any

force

or

energy

involved
.

Fluid Kinematics

Fluids in motion

-

Ideal fluids

-

Streamlines

-

Equation of continuity

-

Bernoulli’s equation

-

Venturi Meter

Ideal Fluids

The motion of real fluids is very complicated.

Using some simplifying assumptions to define
an ideal fluid allows a reasonable description
of much of the behavior of fluids.

An ideal fluid is
incompressible

and

its flow is:

laminar,

non
-
viscous &

irrotational.

Streamlines

A streamline is the path traced out by a tiny
element of the fluid (a fluid “particle”).

The velocity of the fluid particle is tangential
to the streamline.

Streamlines never cross.

A set of streamlines can define a tube of flow,
the borders of which the fluid does not cross

Fluid types

Uniform & non Uniform flow

Changing in space

Changing in time

Laminar & Turbulent flow

(Transition)

Rate of Flow (discharge)

Rate of Flow
-
Continuity Equation

Continuity Equation

In flowing liquids, the mass going

through a certain area equals the

mass going through any other area

Fluid incompressible, so volume
D
V

through
1
in time
D
t same as volume

through
2
, i.e.

D
V = A
1
v
1

D
t = A
2
v
2

D
t

A
1
v
1

= A
2
v
2

Q
1

= Q
2

The
volume flow ra
te
R = Av is

constant (units m
3
/s).

As fluid has constant density (it is

incompressible)

The
mass flow rate

R

= Av

is also constant

(units kg/s).

Mass flow rate

Continuity Equation

Example
1

Example
2