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CAMSin the School of Computing, Engineering and Physical

Sciences

Introductory fluid dynamicsby Dr J. Whitty

321 mmm

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Lessons structure• The lessons will in general be

subdivided in to eight number of parts, viz.:1) Statement of learning objectives2) Points of orders3) 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 exercises7) Summary and feedback8) Formative assessment, via homework task

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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:

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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

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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

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Conservation of massBoth 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.

21 mmmin outmm 3

Consequence??

outin mm i.e.

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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

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Fluids in motionAs 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

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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!

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2. Flow regime’• Laminar

• Turbulent

• Transition flow

Class Exercise:

Use the internet to find defientions of the above!

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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?

zyxv

ppK

zyxv

ppK

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Continuity of flow

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

A1

v2 m/s

v1 m/s

A2

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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 impliestx

tx

tx AAA

332211

xAxAxA ttt 331

221

111

321 mmm and gives: As density and the volume

of then control volume are constant!

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The Continuity Equation:

• We have now we’ve proved the continuity equitation (I wonder why I have spent so many slides on it?)

332211

321

vAvAvA

AAA tx

tx

tx

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

332211 vAvAvA

The Continuity Equation: :

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Example #2

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

20mm DIA

1 m/s

6 m/s

30mm DIA

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Example #2; solution:

• Apply the continuity equation, thus:

3222

3

23

2

22

1

21

20130620

444

v

vD

vD

vD

Hence: 1-

2

22

3 ms25.820

30206

v

Can you drink BEER that quickly?

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Class Problems3. A system has two inlet rates of 3m3/s

& 2m3/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

vout m/s

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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 laminarB1

– The fluid is incompressibleB1

– The fluid is in-viscidB1

1-3321

332211

sm523

QQQ

vAvAvAM1A1

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Class problem; solution #2:

• Apply the continuity equation taking D and 1.25D along as parameter, thus:

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

2

3

32

2

322

537.5

6.15.12.34

6.1)5.1(4

2.34

DQ

QD

QDD

M1

M2

A1

13

322

32

333

ms05.7537.54

4537.5

4

v

vDD

vDvAQ M1

M1

A1

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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]

150oC 25oC

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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

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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