fluid flow

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1

CAMS

in the School of Computing, Engineering and Physical Sciences

Introductory fluid dynamics

by Dr J. Whitty

2

Lessons structure


The lessons will in general be subdivided
in to eight number of parts, viz.:

1)
Statement of learning objectives

2)
Points of orders

3)
Introductory material (Types of flow)

4)
Concept introduction (The conservation of
mass)

5)
Development of related principles (flow
continuity)

6)
Concrete principle examples via


reinforcement examination type exercises

7)
Summary and feedback

8)
Formative assessment, via homework task


3

Learning Objectives


State and use the basic
thermodynamic laws


Derive the conservation of mass


Describe the differences between flow
regimes


Calculate simple fluid flow mechanisms


Evaluate volumetric flow rates in fluid
simple systems



After the session the students
should

be able to:

4

Recap: Laws of thermodynamics


These are quite simply the 4 axioms (self evident
truths) of all modern Physics, they are known as the
four Laws of Thermodynamics and relate to the
quantities of


Zeroth
: Temperature


First:
Energy


Second: Disorder (
Entropy
)


Third:
Balance

of them all

5

Consequences of the first law:

Flow Processes


If we consider the
first law based on
some fluid passing
through a control
volume above a
datum (at sea
-
level)
for consentience.
Application of the
first law, with the
following
assumption:

1.
The mass flow is
constant and equal to
the outlet mass flow

2.
The cross
-
section
properties of the inlet
and outlet are constant

Conservation of Mass

Mass
cannot

be
destroyed

or
created

6

Conservation of mass

Both
Heat
and
fluid flow

must adhere to the principal of
the flow of mass and energy. Here we can consider a
system (sometimes referred to as a
control volume
) with
fluid flow (or heat) in and out of the system

The unit of mass flow the kg
per second (kg/s). Because
speed has magnitude and
direction, it
vector
quantity.

Consequence??

i.e.

7

The Consequence of to
Conservation
of
Mass

1.
The mass (and sometimes volume) flow
rate of a in
-
viscid, incompressible fluid
(like water or oil) is constant.

2.
This principle is one of probably
the

fundamental assumption in the field of
Fluid Mechanics
,
this will now be
explored!

Class Examples Time:

Think of some process which adhere to the above

8

Fluids in motion

As an example of this principle we will investigate the concept of a fluid
(say water) in motion. There is still a little terminology that is
required before we proceed, these being:

1.
Assumptions regarding the fluid in motion, namely:

a)
Viscid

b)
In
-
viscid

2.
Assumptions regarding the type of flow regime’

a)
Laminar

b)
Transition

c)
Turbulent

3.
Assumptions regarding Compressibility:

1.
Compressible, or

2.
In
-
compressible

9

1. Viscosity


The viscosity of a fluid is the internal
resistance to a change in the shape.
Typically viscous fluids are treacle like:
glycerine and thick oils. All fluids have some
type of viscosity, however some fluids have
such small viscosities have (e.g. water, air)
can be considered
in
-
viscid

i.e. the viscosity
of the fluid can be ignored! It is these type of
fluids we considered here.


Hence we have:

1.
Viscid fluids (includes fluid viscosity effects)

2.
In
-
viscid fluids (neglects fluid viscosity effects)

Since the
math

is considerably reduced when in
-
viscid fluids are concerned it is these types we
consider!

10

2. Flow regime’


Laminar




Turbulent




Transition flow

Class Exercise:

Use the internet to find defientions of the above!

11

3.
Compressibility


Incompressible fluid:
Where the density of the fluid
remains
constant
!
(This course)


Incompressible fluid:
Where the density of the fluid
changes
during the flow process!
(Not
this course
)


When the
Compressibility

(Bulk) Modulus
is?


Class Question:

What?

12

Continuity of flow


For the system shown, given that the
flow is laminar, in
-
viscid and
incompressible, find the flow rate at the
outlet.

A
1

v
2

m/s

v
1

m/s

A
2

13

Continuity of flow;
Solution:


Here we could just apply the
conservation of mass, as we know it is a
consequence of the first law of
thermodynamics, thus:

which implies

and gives:

As density and the volume
of then control volume are
constant!

14

The Continuity Equation
:


We have now we’ve proved the
continuity equitation

(I wonder why I
have spent so many slides on it?)

Using the fact that.
The flow is in
-
compressible:


The Continuity Equation
:

:


15

Example #2


Evaluate the velocity of the fluid exiting
the barrel of beer:

20mm DIA

1 m/s

6

m/s

30mm DIA

16

Example #2;
solution:


Apply the continuity equation, thus:

Hence:


Can you drink BEER that quickly
?


17

Class

Problems

3.
A system has two inlet rates of 3m
3
/s &
2m
3
/s what is the approximate output
velocity [2]; and what assumptions did you
make [3]?

4.
For the system shown, determine the
volumetric flow rate and velocity at the out
-
let. Given the large diameter pipe is 1.25
that of the smaller.

3.2m/s

1.6m/s

v
out

m/s

18

Class

problem; solution #4:


Here were are given the volumetric flow
rate, hence by continuity we have:





There are three assumptions in place
here:


The flow regime is laminar
B1


The fluid is incompressible
B1


The fluid is in
-
viscid
B1


M1A1

19

Class

problem; solution #2:


Apply the continuity equation taking
D
and
1.25
D

along as parameter, thus:





The required velocity can be found from the flow
rate thus:


M1

M2

A1

M1

M1

A1

20

Examination

type questions

1.
Explain
, using cogent examples:
three

laws of thermodynamics [6].

a)
Use formulae to describe
three

mechanisms of
heat transfer [6].

b)
Find the total heat lost an asbestos (thermal
conductivity 0.15W/mK) reinforced steel wall
(thermal conductivity 50W/mK), given that the
concrete is twice the thickness of the steel. [8]


150
o
C

25
o
C

21

Examination

type questions

2.
State three states of matter. [3]

a)
Explain the meaning of incompressible flow
[2].

b)
Given that the large pipe is 1.4 times the
diameter of the small pipe evaluate the
velocity at the output [12],






c) Clearly state the assumptions of the
modelling process [3].

3.4m/s

2.1m/s

22

Summary


Have we met our learning objectives:
specifically
, are you now able to do:


State and use the basic thermodynamic
laws


Derive the conservation of mass


Describe the differences between flow
regimes


Calculate simple fluid flow mechanisms


Evaluate volumetric flow rates in fluid
simple systems