Basic fluid mechanics for civil engineers

Maxime Nicolas

To cite this version:

Maxime Nicolas. Basic fluid mechanics for civil engineers. Engineering school. France. 2016.

HAL Id: cel-01440549

https://hal.archives-ouvertes.fr/cel-01440549

Submitted on 25 Jan 2017

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destin´ee au d´epˆot et `a la diffusion de documents

scientifiques de niveau recherche, publi´es ou non,

´emanant des ´etablissements d’enseignement et de

recherche fran¸cais ou ´etrangers, des laboratoires

publics ou priv´es.

Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0

International License

Basic fluid mechanics for civil engineers

Maxime Nicolas

maxime.nicolas@univ-amu.fr

D´

epartement g´

enie civil

september–december 2016

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

1 / 49

Course 1 outline

1

Preamble

Course schedule

Online

Working advices

Course outline

2

Introduction and basic concepts

Description of a fluid

Maths for fluid mechanics

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

2 / 49

Preamble

PREAMBLE

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

3 / 49

Preamble

Course schedule

Course syllabus

Schedule:

10 lectures

10 workshops

Assessment and exam:

activity

homework

final exam (Dec. 5th)

flash quiz

M. Nicolas (Polytech Marseille GC3A)

percentage

20%

bonus +1 if written in english

80%

+1 point on the final grade

Fluid mechanics

september–december 2016

4 / 49

Preamble

Online

Online

This course is available on ENT/AmeTice :

Sciences & technologies � Polytech � G´enie civil �

[16] - S5 - JGC51B - M´ecanique des fluides (Maxime Nicolas)

with

slides

workshops texts

equation forms

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

5 / 49

Preamble

Working advices

Working advices

personal work is essential

read your notes before the next class and before the workshop

be curious

work for you (not for the grade)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

6 / 49

Preamble

Course outline

Course outline

1

2

3

4

5

6

7

8

9

10

Introduction and basic concepts

vector calculus

Statics

hydrostatic pressure, Archimede’s principle

Kinematics

Euler and Langrage description, mass conservation

Balance equations

mass and momentum cons. equation

Flows classification and Bernoulli

Venturi e↵ect

The Navier-Stokes equation

Poiseuille and Couette flows

The Stokes equation

Flow Sedimentation

Non newtonian fluids

Concrete flows

Flow in porous media

Darcy

Surface tension e↵ects

Capillarity

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

7 / 49

Introduction and basic concepts

INTRODUCTION AND BASIC CONCEPTS

Description of a fluid

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

8 / 49

Introduction and basic concepts

●○

What is fluid mechanics?

Physics

continuum mech.

solid mech.

fluid mech.

aerodynamics

supersonic flows

M. Nicolas (Polytech Marseille GC3A)

waves

viscous flows

Fluid mechanics

september–december 2016

9 / 49

Introduction and basic concepts

What is fluid mechanics?

○●

Fluid mechanics is the mechanical science for gazes or liquids, at rest or

flowing.

Large set of applications :

blood flow

atmosphere flows, oceanic flows, lava flows

pipe flow (water, oil, vapor)

flight (birds, planes)

pumping

dams, harbours

...

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

10 / 49

Introduction and basic concepts

Large atmospheric phenomena

Ouragan Katrina, 29 aoˆ

ut 2005

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

11 / 49

Introduction and basic concepts

FM for civil engineering: dams

Hoover dam, 1935

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

12 / 49

Introduction and basic concepts

FM for civil engineering: wind e↵ects on structures

from timberframehome.wordpress.com

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

13 / 49

Introduction and basic concepts

FM for civil engineering: harbor structures

from www.marseille-port.fr

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

14 / 49

Introduction and basic concepts

FM for civil engineering: concrete flows

from http://www.chantiersdefrance.fr

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

15 / 49

Introduction

basicmixtures

concepts exhibit

Description of a fluid

ded periods of time. Some plastics,

lead, andand

slurry

Liquid

Gas

ehavior. Such borderline cases are beyond the scope of this text. The

will deal with in this text will be clearly recognizable as fluids.

olecular bonds are strongest in solids and weakest in gases. One

s that molecules in solids are closely packed together, whereas in

ey are separated by relatively large distances (Fig. 1–5).

FIGURE 1–4

olecules in a solid are arranged in a pattern that is repeated throughUnlike a liquid, a gas does not form a

ause of the small distances between molecules in a solid, the attracfree surface, and it expands to fill the

entire available space.

es of molecules on each other are large and keep the molecules at

What is a fluid?

(a)

(b)

(c)

FIGURE 1–5

The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions

in a solid, (b) groups of molecules move about each other in the liquid phase, and

(c) molecules move about at random in the gas phase.

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

16 / 49

Introduction and basic concepts

Description of a fluid

Main concepts

density

stresses and pressure

viscosity

superficial tension

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

17 / 49

Introduction and basic concepts

Description of a fluid

density

density = weight per unit volume

unit : kg⋅m−3

fluid

air

water

concrete

molten iron

density in kg⋅m−3

1.29

1 000

2 500

≈ 7 000

Notice: density decreases with temperature increase

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

18 / 49

Introduction and basic concepts

Description of a fluid

Stress

�

→

Elementary force F applying on an elementary surface S.

n

𝛿F

𝛿S

Ratio is

the stress vector.

Standard unit : Pa (pascal).

M. Nicolas (Polytech Marseille GC3A)

�

→

�

→= F

S

Fluid mechanics

1 Pa = 1 N⋅m−2 = 1 kg⋅m−1 ⋅s−2

september–december 2016

19 / 49

Introduction and basic concepts

Description of a fluid

Stress

→

The surface element S is oriented by a unit vector �

n.

�

→

n is normal (perpendicular) to the tangential plane.

�

→=�

→+�

→

n

with

→

→

�

→ = (�

→⋅�

n )�

n

n

t

→ �

→

�

→=�

→−�

→ = (�

→⋅�

t)t

t

n

n

𝛿S

t

stress vector = normal stress ( ⊥) + shear stress (//)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

20 / 49

Introduction and basic concepts

Description of a fluid

Pressure

The pressure is a normal stress.

Notation : p

S.I. unit : pascal (Pa)

1 Pa = 1 N⋅m−2 = 1 kg⋅m−1 ⋅s−2

basic interpretation: normal force applied on a surface

The pressure in a fluid is an isotropic stress: its intensity does not depend

on the direction.

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

21 / 49

Introduction and basic concepts

Description of a fluid

Pressure examples

m= 1500 kg with load

H

p(H)

S = 0.5 m2

p

p(H)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

22 / 49

Introduction and basic concepts

Description of a fluid

viscosity

A macroscopic view on viscosity :

moving plate

U

F

u(y)

h

velocity profile

fixed boundary

Tangential (shear) stress:

Shear rate: ˙ = Uh

For a newtonian fluid :

t

=⌧ =

F

A

⌧ =⌘ ˙

⌘ is the dynamic viscosity of the fluid

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

23 / 49

Introduction and basic concepts

Description of a fluid

viscosity

Standard unit: [⌘]=Pa⋅s

fluid

air

water

blood

honey

fresh concrete

1 Pa⋅s=1 kg⋅m−1 ⋅ s−1

⌘ (Pa⋅s)

1.8 10−5

10−3

6 10−3

10

5–25 Bnon-newtonian fluid

Also useful : kinematic viscosity

with [⌫]=m2 ⋅s−1

M. Nicolas (Polytech Marseille GC3A)

⌫=

⌘

⇢

Fluid mechanics

september–december 2016

24 / 49

Maxime Nicolas

To cite this version:

Maxime Nicolas. Basic fluid mechanics for civil engineers. Engineering school. France. 2016.

HAL Id: cel-01440549

https://hal.archives-ouvertes.fr/cel-01440549

Submitted on 25 Jan 2017

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destin´ee au d´epˆot et `a la diffusion de documents

scientifiques de niveau recherche, publi´es ou non,

´emanant des ´etablissements d’enseignement et de

recherche fran¸cais ou ´etrangers, des laboratoires

publics ou priv´es.

Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0

International License

Basic fluid mechanics for civil engineers

Maxime Nicolas

maxime.nicolas@univ-amu.fr

D´

epartement g´

enie civil

september–december 2016

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

1 / 49

Course 1 outline

1

Preamble

Course schedule

Online

Working advices

Course outline

2

Introduction and basic concepts

Description of a fluid

Maths for fluid mechanics

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

2 / 49

Preamble

PREAMBLE

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

3 / 49

Preamble

Course schedule

Course syllabus

Schedule:

10 lectures

10 workshops

Assessment and exam:

activity

homework

final exam (Dec. 5th)

flash quiz

M. Nicolas (Polytech Marseille GC3A)

percentage

20%

bonus +1 if written in english

80%

+1 point on the final grade

Fluid mechanics

september–december 2016

4 / 49

Preamble

Online

Online

This course is available on ENT/AmeTice :

Sciences & technologies � Polytech � G´enie civil �

[16] - S5 - JGC51B - M´ecanique des fluides (Maxime Nicolas)

with

slides

workshops texts

equation forms

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

5 / 49

Preamble

Working advices

Working advices

personal work is essential

read your notes before the next class and before the workshop

be curious

work for you (not for the grade)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

6 / 49

Preamble

Course outline

Course outline

1

2

3

4

5

6

7

8

9

10

Introduction and basic concepts

vector calculus

Statics

hydrostatic pressure, Archimede’s principle

Kinematics

Euler and Langrage description, mass conservation

Balance equations

mass and momentum cons. equation

Flows classification and Bernoulli

Venturi e↵ect

The Navier-Stokes equation

Poiseuille and Couette flows

The Stokes equation

Flow Sedimentation

Non newtonian fluids

Concrete flows

Flow in porous media

Darcy

Surface tension e↵ects

Capillarity

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

7 / 49

Introduction and basic concepts

INTRODUCTION AND BASIC CONCEPTS

Description of a fluid

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

8 / 49

Introduction and basic concepts

●○

What is fluid mechanics?

Physics

continuum mech.

solid mech.

fluid mech.

aerodynamics

supersonic flows

M. Nicolas (Polytech Marseille GC3A)

waves

viscous flows

Fluid mechanics

september–december 2016

9 / 49

Introduction and basic concepts

What is fluid mechanics?

○●

Fluid mechanics is the mechanical science for gazes or liquids, at rest or

flowing.

Large set of applications :

blood flow

atmosphere flows, oceanic flows, lava flows

pipe flow (water, oil, vapor)

flight (birds, planes)

pumping

dams, harbours

...

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

10 / 49

Introduction and basic concepts

Large atmospheric phenomena

Ouragan Katrina, 29 aoˆ

ut 2005

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

11 / 49

Introduction and basic concepts

FM for civil engineering: dams

Hoover dam, 1935

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

12 / 49

Introduction and basic concepts

FM for civil engineering: wind e↵ects on structures

from timberframehome.wordpress.com

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

13 / 49

Introduction and basic concepts

FM for civil engineering: harbor structures

from www.marseille-port.fr

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

14 / 49

Introduction and basic concepts

FM for civil engineering: concrete flows

from http://www.chantiersdefrance.fr

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

15 / 49

Introduction

basicmixtures

concepts exhibit

Description of a fluid

ded periods of time. Some plastics,

lead, andand

slurry

Liquid

Gas

ehavior. Such borderline cases are beyond the scope of this text. The

will deal with in this text will be clearly recognizable as fluids.

olecular bonds are strongest in solids and weakest in gases. One

s that molecules in solids are closely packed together, whereas in

ey are separated by relatively large distances (Fig. 1–5).

FIGURE 1–4

olecules in a solid are arranged in a pattern that is repeated throughUnlike a liquid, a gas does not form a

ause of the small distances between molecules in a solid, the attracfree surface, and it expands to fill the

entire available space.

es of molecules on each other are large and keep the molecules at

What is a fluid?

(a)

(b)

(c)

FIGURE 1–5

The arrangement of atoms in different phases: (a) molecules are at relatively fixed positions

in a solid, (b) groups of molecules move about each other in the liquid phase, and

(c) molecules move about at random in the gas phase.

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

16 / 49

Introduction and basic concepts

Description of a fluid

Main concepts

density

stresses and pressure

viscosity

superficial tension

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

17 / 49

Introduction and basic concepts

Description of a fluid

density

density = weight per unit volume

unit : kg⋅m−3

fluid

air

water

concrete

molten iron

density in kg⋅m−3

1.29

1 000

2 500

≈ 7 000

Notice: density decreases with temperature increase

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

18 / 49

Introduction and basic concepts

Description of a fluid

Stress

�

→

Elementary force F applying on an elementary surface S.

n

𝛿F

𝛿S

Ratio is

the stress vector.

Standard unit : Pa (pascal).

M. Nicolas (Polytech Marseille GC3A)

�

→

�

→= F

S

Fluid mechanics

1 Pa = 1 N⋅m−2 = 1 kg⋅m−1 ⋅s−2

september–december 2016

19 / 49

Introduction and basic concepts

Description of a fluid

Stress

→

The surface element S is oriented by a unit vector �

n.

�

→

n is normal (perpendicular) to the tangential plane.

�

→=�

→+�

→

n

with

→

→

�

→ = (�

→⋅�

n )�

n

n

t

→ �

→

�

→=�

→−�

→ = (�

→⋅�

t)t

t

n

n

𝛿S

t

stress vector = normal stress ( ⊥) + shear stress (//)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

20 / 49

Introduction and basic concepts

Description of a fluid

Pressure

The pressure is a normal stress.

Notation : p

S.I. unit : pascal (Pa)

1 Pa = 1 N⋅m−2 = 1 kg⋅m−1 ⋅s−2

basic interpretation: normal force applied on a surface

The pressure in a fluid is an isotropic stress: its intensity does not depend

on the direction.

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

21 / 49

Introduction and basic concepts

Description of a fluid

Pressure examples

m= 1500 kg with load

H

p(H)

S = 0.5 m2

p

p(H)

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

22 / 49

Introduction and basic concepts

Description of a fluid

viscosity

A macroscopic view on viscosity :

moving plate

U

F

u(y)

h

velocity profile

fixed boundary

Tangential (shear) stress:

Shear rate: ˙ = Uh

For a newtonian fluid :

t

=⌧ =

F

A

⌧ =⌘ ˙

⌘ is the dynamic viscosity of the fluid

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

23 / 49

Introduction and basic concepts

Description of a fluid

viscosity

Standard unit: [⌘]=Pa⋅s

fluid

air

water

blood

honey

fresh concrete

1 Pa⋅s=1 kg⋅m−1 ⋅ s−1

⌘ (Pa⋅s)

1.8 10−5

10−3

6 10−3

10

5–25 Bnon-newtonian fluid

Also useful : kinematic viscosity

with [⌫]=m2 ⋅s−1

M. Nicolas (Polytech Marseille GC3A)

⌫=

⌘

⇢

Fluid mechanics

september–december 2016

24 / 49

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