Fluid Dynamics

1
Fluid Dynamics
2
Fluid Dynamics
Fluid dynamics is the study of how fluids (gases
or liquids) flow. Because water is such a common
fluid, fluid dynamics is often called
hydrodynamics.
3
Discharge
When fluid flows through a pipe, the flow or
discharge (J) is the mass J (or volume Q) of
fluid that passes a given point per unit of time.
4
Discharge
Mathematically Q Av
5
Discharge
Describing discharge as mass per unit time is
actually more correct, but if the pipe is full of
an incompressible (constant r) fluid then either
description is fine.
6
Discharge
i.e. J Dm/t rDV/t rADl/t rAv Since r is
usually constant, discharge in terms of volume
is Q Av
7
Equation of continuity
If an incompressible fluid fills a pipe and flows
through it, the discharge stays constant even if
the diameter of the pipe changes.
8
Equation of continuity
Mathematically Q A1v1 A2v2 constant
9
Wind Tunnels
We can study fluid flow patterns with wind
tunnels
10
Wind Tunnels
There are many types.
11
Wind Tunnels
Some are wicked cool!
12
Wind Tunnels
Some contain wicked cool things!
13
Wind Tunnels
After designing models based on computed
calculations of flow characteristics, the
predictions can be checked with a flow test.
http//www.esa.int/esaCP/ESA9DBG18ZC_index_0.html
14
Types of Fluid Flow
There are two main types of fluid flow
Laminar
and
Turbulent
15
Laminar Flow
Laminar flow (AKA streamline flow) occurs when
the particles of the fluid follow smooth,
noncrossing paths.
16
Laminar Flow
Note that during laminar flow, neighboring layers
of the fluid slide by each other smoothly.
17
Laminar Flow
Note that this is a shearing process.
F
18
Laminar Flow
To study this process, two plates are separated
by a thin layer of liquid.
19
Laminar Flow
A force is applied to the top plate to make it
move.
F
20
The rapidity of the shearing motion is
characterized by the shear rate of the two plates
and the fluid between them.
F
21
Shear rate speed of top plate
distance between plates
Shear rate v/L Des / t
F
22
The viscosity of a fluid is the shear stress
required to produce a unit shear rate.
F
23
h viscosity shear stress/shear rate.
h (F/A) / (v/L)
F
24
h viscosity shear stress/shear rate.
h (F/A) / (v/L) (FL) / (vA)
FYI
h the lower Greek letter eta
F
25
F a vA / L for any given fluid. So the larger
the h value, the greater the force resisting the
attempted shear under a given set of conditions.
(i.e. The fluid is stickier.)
F
26
For liquids, the viscosity results from
attractive forces between the molecules. For
gases, the viscosity results from collisions
between the molecules.
F
27
The SI unit for h is N.s/m2, or Pa.s. This is
called the poiseuille (Pl). Other units are the
cgs unit the poise (P), for which 1 P 0.1 Pl,
and prefix versions of each.
F
28
The greater the viscosity in a fluid, the greater
the heat generated as it is sheared under a given
set of conditions.
F
29
Because of viscosity, it takes a pressure
difference at the ends of a horizontal pipe to
have laminar fluid flow through it at a steady
rate. A French scientist named Poiseuille
studied this in the 1800s and developed the
formula that bears his name Q (pr 4(P1-P2))
/ (8hL)
30
Q (pr 4(P1-P2)) / (8hL) All My Loving Pi r
fourth delta P Over 8 eta L Shows how fast Vs
flowing Thats Q
31
Turbulent Flow
When fluid flows beyond a certain speed, the
laminar flow breaks down into turbulent flow.
32
Turbulent flow is characterized by small
whirlpools called eddies, which consume an
enormous amount of energy. This increases the
drag on the object in the fluid flow far above
the drag created by viscosity during streamline
(laminar) flow. For liquids in a pipe, this
translates to a need for a much higher (and less
predictable) ____________ to maintain the flow.
pressure
33
Reynold's Number
The Reynolds Number (NR) is a dimensionless
experimental number that gives an indication of
the velocity at which turbulence will occur in a
fluid.
34
Reynold's Number
Mathematically NR rvD/h Fluid flow will
usually be laminar if NR does not exceed about
2000 for fluid flowing through a pipe, or about
10 for obstacles.
35
Bernoulli's Principle
In the 1700s, a mathematician named Daniel
Bernoulli studied the pressure associated
with moving fluids and came to a
startling conclusion
http//www-history.mcs.st-and.ac.uk/history/Mathem
aticians/Bernoulli_Daniel.html
36
Bernoulli's Principle
Bernoullis Principle basically states that As a
fluids velocity increases, its internal pressure
decreases!
37
Bernoulli's Principle
Bernoullis Principle applies to a variety of
phenomena.
38
Bernoulli's Equation
Mathematically P1 ½ rv12 rgh1 P2 ½ rv22
rgh2
OK.
But why???
39
Bernoulli's Equation
Bernoullis Equation is really a restatement of
the Law of Conservation of Energy The total
energy of a closed system remains constant. (This
is true unless there is a ____________ change.)
P1 ½ rv12 rgh1 P2 ½ rv22 rgh2
nuclear
40
Since work is done whenever a force is applied
through a distance, work is done whenever
pressure forces a volume of fluid to move as
well. P1 ½ rv12 rgh1 P2 ½ rv22
rgh2
W F x d
W P x V
Note W (F/A) x A x Dl
A A
41
Also, since work must be done to accelerate an
object, faster moving objects have more kinetic
energy. By replacing the m in the equation with
rADl, we can see that P1 ½ rv12
rgh1 P2 ½ rv22 rgh2
W DKE ½ mv2
W DKE ½ rVv2
42
Lastly, since work must be done to raise an
object, potential energy may be exchanged for
kinetic energy. By replacing the m in the
equation with rADl, we can see that P1
½ rv12 rgh1 P2 ½ rv22 rgh2
W DPE DKE mgDh
W DPE DKE rVgDh
43
So all the terms in Bernoullis Equation are
really energy terms associated with a given
volume movement. P1V ½ rVv12 rVgh1 Constant
This becomes P1 ½ rv12 rgh1 Constant / V
44
Bernoulli's Equation
Note that Bernoullis Equation ignores viscosity
and compressibility. Reality is more closely
modeled with the Navier-Stokes equation, but that
is beyond the scope of this course.
45
"That we have written an equation does not remove
from the flow of fluids its charm or mystery or
its surprise." --Richard Feynman 1964
http//jef.raskincenter.org/published/coanda_effec
t.html
http//en.wikipedia.org/wiki/Richard_Feynman
46
Torricelli's Theorem
Long before Bernoulli entered the world,
Torricelli realized that if a fluid were to flow
from a w-i-d-e barrel, the fluid velocity would
depend on the height of the fluid above the
spigot. He determined that the formula was

v
47
Torricelli's Theorem
Long before Bernoulli entered the world,
Torricelli realized that if a fluid were to flow
from a w-i-d-e barrel, the fluid velocity would
depend on the height of the fluid above the
spigot. He determined that the formula was

v v2gh
48
Torricelli's Theorem
Why would that be? Well, if we modify Bernoulli
we can derive this! (Note essentially we are
giving up _______, and gaining _______.)
PE
KE
P1 ½ rv12 rgh1 P2 ½ rv22 rgh2
Since the air pressure doesnt change much,
P1 ½ rv12 rgh1 P2 ½ rv22 rgh2
49
Torricelli's Theorem
Since the top is still and the bottom is
the bottom P1 ½
rv12 rgh1 P2 ½ rv22 rgh2
Since the fluid is considered to be
incompressible P1 ½ rv12
rgh1 P2 ½ rv22 rgh2
50
Torricelli's Theorem
By rearrangement
v v2gh
So Torricelli is an example of Bernoulli. How
about others?
51
Bernoulli's Principle
Bernoullis Principle explains the dynamic lift
of flying birds and planes, venturi tubes (car
carburetors, venturi meters, atomizers), air
circulation in burrows, curveballs, many musical
instruments, and TIAs.
52
Bernoulli's Principle
Bernoullis Principle helps to explain the
dynamic lift that supports birds and airplanes.
53
Bernoulli's Principle
Note also that there are MANY ways to look at
flight. Despite the differences in approach,
they (the correct interpretations) all work.
http//hyperphysics.phy-astr.gsu.edu/hbase/fluids/
airfoil.htmlc1
54
Bernoulli's Principle
"In aerodynamics, theory is what makes the
invisible plain. Trying to fly an airplane
without theory is like getting into a fistfight
with a poltergeist." --David Thornburg 1992.
http//jef.raskincenter.org/published/coanda_effec
t.html
55
Bernoulli's Principle
Dynamic lift occurs when a moving fluid is turned
by a solid object.
http//www.av8n.com/irro/lecture_e.html
56
Bernoulli's Principle
Notice that the fluid travels faster over this
wing, producing a net upward force, or lift.
http//www.av8n.com/irro/lecture_e.html
57
Bernoulli's Principle
Lets study this a bit
Link to http//www.grc.nasa.gov/WWW/K-12/airplan
e/wrong2.html
58
Bernoulli's Principle
Question Would this undercambered wing generate
more or less lift than one which had a flat
bottom?
More!
http//jef.raskincenter.org/published/coanda_effec
t.html
Link to http//www.grc.nasa.gov/WWW/K-12/airplan
e/wrong2.html
59
Note

1. The airfoil does NOT need to be curved.
2. Both the upper and lower surfaces affect the
   turning of the fluid.

http//en.wikipedia.org/wiki/Airfoil
Link to http//www.grc.nasa.gov/WWW/K-12/airplan
e/wrong2.html
60
The Coanda effect works like this A fluid
moving by a straight object moves straight.
61
If an object is bent into the path of the fluid,
the fluid bends to follow the object.
62
But if an object is bent away from the path of
the fluid, the fluid still bends to follow the
object!
63
The Coanda effect was named after the Romanian
inventor Henri Coanda, who helped develop some of
the first aircraft to utilize the jet engine.
http//en.wikipedia.org/wiki/CoandC483_effect_mo
vies
64
Curve Balls
Curve balls curve because of Bernoulli.
http//hyperphysics.phy-astr.gsu.edu/hbase/fluids/
kutta.htmlc1
65
Atomizers
Atomizers work because of Bernoulli.
http//hyperphysics.phy-astr.gsu.edu/hbase/fluids/
kutta.htmlc1
66
Venturi Tubes
Venturi tubes work because of Bernoulli.
http//www.physics.lsa.umich.edu/demolab/demo.asp?
id27
67
Venturi Tubes
Aspirators work because of Bernoulli.
http//hyperphysics.phy-astr.gsu.edu/hbase/fluids/
aspirv.htmlc1