School of Jet Propulsion

1

FLUID MECHANICS

• School of Jet Propulsion
• Beihang University.

2
Chapter 1 Introduction

• 1.1 Preliminary Remarks
• When you think about it, almost everything on
  this planet either is a fluid or moves within or
  near a fluid.
• -Frank M.
  White

What is a fluid?
3
The concept of a fluid

• A solid can resist a shear stress(????)
• by a static deformation, a fluid can not.
• Any shear stress applied to a fluid, no matter
  how small, will result in motion of that fluid.
• The fluid moves and deforms continuously as long
  as the shear is applied.

4
What is Fluid Mechanics

• Fluid Mechanics is the study of fluid either
  in motion (Fluid Dynamics ?????) or at rest(Fluid
  Statics ?????) and subsequent effects of the
  fluid upon the boundaries, which may be either
  solid surfaces or interfaces with other fluids.

5
The famous collapse of the Tacoma Narrow Bridge
in 1940
Curved shoot (Banana shoot)
why
Nospin
Spin
6
Boeing 747 70.764.4 19.41 (m) 395 000kg
An-225 8488.418.1 (m) 600,000kg
How can the airplane fly?
Drag Lift
7
(No Transcript)
8
The engine of a turbofan(??) jet
9

10
History and Scope of Fluid Mechanics

• Pre-history
• Sailing ships with oars(??) and irrigation system
  were both known in prehistory

11
Archimedes(285-212 BC)

• Parallelogram law for addition of vectors

• Law of buoyancy

12
Leonardo da Vinci(1452-1519)

• Equation of conservation of mass in
  one-dimensional steady flow

Experimentalist
Turbulence
13
Isaac Newton(1642-1727)
Laws of motion
Laws of viscosity of Newtonian fluid
14

18th century
Mathematicians

• Euler(??) Euler equation
• Bernoulli (???) Bernoulli equation

Frictionless(??) flow solutions
DAlembert(????) DAlembert
paradox(??,??)
Engineers Hydraulics (???)relaying on experiment
Channels ,Ship resistance, Pipe flows,Wave turbine
Pitot Venturi Torricelli
Poiseuille
15
19th century

• Navier (1785-1836)
• Stokes (1819-1905)
• N-S equation viscous flow solution

Reynolds (1842-1912) Turbulence Famous
experiment on transition Reynolds Number
16
20th century

• Ludwig Prandtl (1875-1953)
• Boundary theory(1904)
• To be the single most important tool in modern
  flow analysis.
• The father of modern fluid mechanics

Laid foundation for the present state of the art
in fluid mechanics
Vonkarman (1881-1963)

• I.taylor(1886-1975)

17
1.2 The Fluid as a Continuum (????)
Density(??)

• Elemental volume(?????????)
• Large enough in microscope(??)
• 10-9mm3 of air at standard conditions contains
  approximately 3107 molecules.

Small enough in macroscope(??). Most
engineering problems are concerned with physical
dimensions much larger than this limiting volume.
So density is essentially a point function and
fluid properties can be thought of as varying
continually in space .
18
The elemental volume must be small enough in
macroscope
Such a fluid is called a continuum, which simply
means that its variation in properties is so
smooth that the differential calculus can be used
to analyze the substance.
19
1.3 Some Properties of fluids

• 1.viscosity(??)
• Definition When a fluid is sheared(??), it
  begins to move. Subsequently, a pair of forces
  appear on the shear surface, which resists the
  shear motion of the fluid. This is called
  viscosity

This resistant force is shear stress.(????,?????)
In fact, this shear motion of a fluid is a kind
of deformation(??)
The nature of viscosity
For liquid is cohesion(??)(movie)
For gas is the transport of momentum(????)(movie)
20
Newtonian law of viscosity (??????,???????)
Shear stress
Velocity gradient

• m Coefficient of viscosity
  (????)FT/L2
• n m / r Kinematic viscosity (???????)L2/T

The linear fluid, which follow Newtonian
resistance law,is called Newtonian flow.
(?????????)
The velocity gradient is in fact a kind of
deformation.
Real fluid (Viscous) , Ideal fluid (Inviscid
Frictionless)
21
2. Compressibility(???)

• Incompressible(???) r const
• Most liquid flows are treated as incompressible.
• Only 1 percent increase if pressure increase by
  220

Compressible(???) r r (P.T) Gases can also be
treated as incompressible when their velocity is
less than 0.3 Ma numbers
3. State Relations for Gases Perfect-gas
Law(????????)
22
4.Thermal Conductivity(???)
Fouriers law of heat conduction
heat flux in n direction per unit area k
coefficient of thermal conductivity T
temperature n direction of heat transfer
23
1.4 Two different points of view in analyzing
problems in mechanics

• The Eulerian view (????)and the Lagrangian view
  (??????)
• The Eulerian view is concerned with the field of
  flow, appropriate to fluid mechanics.

The Lagrangian view follows an individual
particle moving though the flow,appropriate to
solid mechanics.
The contrast of two frames
24
Flow classification(????)
According to Eulerian view, any property is
function of coordinates(space) and time. In
Cartesian system (?????) ,it can be expressed as
f(x,y,z,t)
x,y,z,t Eulerian variable component ( ????)

• f Function of only one coordinate component,
  one-dimensional ( ?? 1-D). In the like manner,
  two-dimensional ( ?? 2-D) , three-dimensional (
  ?? 3-D )

Function of time unsteady
(???) Otherwise steady (??)
25
One Two dimensional Three
Steady Unsteady
Compressible Incompressible
Viscous Inviscid
26
1.5 Streamline(??),Pathline(??) Flowfield (??)

• What is a
• streamline

A streamline is the line everywhere tangent to
the velocity vector at a given instant.
27

What is a pathline

• A pathline is the actual path traversed by a
  given fluid particles.

Pathlines in unsteady flow
Pathlines in steady flow
For steady flow Streamline Pathline
28
Flow Pattern (?????????) Stream surface(??)
Streamtube (??)
Flow pattern a set of streamlines
Streamsurface a collection of all the
streamlines passing through a line which is not a
streamline.
Streamtube a closed collection of streamlines.
Stream line can not intersect(??), except for
singularity point(??)
29
Flow field (??) In a given flow situation, the
properties of the fluid are functions of position
and time, namely space-time distributions of the
fluid properties.
30
Streamline equation(????)
ds -gt Infinitesimal (???)
31
Example
Given the steady two-dimensional velocity
distribution ukx,v-ky,w0,where k is a positive
constant. Compute and plot the streamlines of the
flow,including direction.
Solution Since time (t) does not appear
explicitly,the motion is steady,so that
streamlines,pathlines will coincide.Since w0,the
motion is two-dimensional.
Integrating
Hyperbolas(???)
32
Direction ukx, v-ky Quadrant I (????)
(xgt0,ygt0) ugt0, vlt0
At the point o u v 0 Singularity point, (?)
33
1.5 Surface force(???) and body
force(???,???)
Surface force acts continuously on the side
surfaces of fluid elements. Pressure, friction
. Contact surface force per unit area(
????) ( ??)
Body force acts on the entire mass of the
element. Gravity , electromagnetic. No
cotact Per unit mass(????) g
34
Home work 1. Given the velocity distribution u
- c y, v c x , w 0 Where c is a positive
constant. Compute and plot the streamlines of the
flow. 2. Given velocity distribution u x t
, v - y t , w 0 ( t is time) Find the
streamline passing through point(-1,-1) at the
instant t0.