Basic fluid mechanics for civil engineers

Basic fluid mechanics for civil engineers
Maxime Nicolas

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


D´

epartement g´
enie civil

september–december 2016

M. Nicolas (Polytech Marseille GC3A)

Fluid mechanics

september–december 2016

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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

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Preamble

PREAMBLE

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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

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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

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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)

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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

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Introduction and basic concepts

INTRODUCTION AND BASIC CONCEPTS
Description of a fluid

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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

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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
...

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Introduction and basic concepts

Large atmospheric phenomena

Ouragan Katrina, 29 aoˆ
ut 2005

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Introduction and basic concepts

FM for civil engineering: dams
Hoover dam, 1935

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Introduction and basic concepts

FM for civil engineering: wind e↵ects on structures

from timberframehome.wordpress.com

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Introduction and basic concepts

FM for civil engineering: harbor structures

from www.marseille-port.fr

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Introduction and basic concepts

FM for civil engineering: concrete flows

from

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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.

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Introduction and basic concepts

Description of a fluid

Main concepts

density

stresses and pressure
viscosity
superficial tension

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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

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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
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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 (//)

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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.

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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)

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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
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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)

⌫=

⌘
⇢

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