Transcript Introduction to Fluid Mechanics

Introduction to Fluid Mechanics
Bellagio Fountain
© 2006 Baylor University
Slide 1
Lecture 8
Introduction to Fluid Mechanics
Approximate Running Time - 21 minutes
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Presented by
Department of Mechanical Engineering
Baylor University
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© 2006 Baylor University
Slide 2
Lecture 8 Topics
•Outline
– Measuring Devices for
Measuring Drag
– Basics of Fluid Mechanics
– Flight Characteristics of
Baseballs & Golf Balls
Dr. Carolyn Skurla
Speaking
© 2006 Baylor University
Slide 3
Lab: Drag Force Experiment
• Performing a fluid mechanics experiment
– Collect experimental data
– Perform integration of experimental data
• Equipment:
– Wind tunnel
– Cylinder
– Pressure
transducer
– Pitot-static
tube
© 2006 Baylor University
Slide 4
So, What is Fluid Mechanics?
• The study of fluids in motion
– Solid -> Can resist a shear stress by a static deformation
– Fluid -> Cannot resist a shear stress
• Any shear stress applied to a fluid will result in motion of that fluid
• There are two classes of fluids:
– Liquids
– Gases
© 2006 Baylor University
(White, 1994)
Slide 5
Thermodynamic Properties of a
Fluid
• Pressure, p
– Compression stress at a point in a fluid
– Differences, or gradients, of pressure often drive
a fluid flow
• Temperature, T
– Measure of internal energy level of a fluid
© 2006 Baylor University
Slide 6
Thermodynamic Properties of a
Fluid
• Density, 
– Mass per unit volume
• Highly variable in gases (i.e.,  =f(p))
• Nearly constant in liquids
– Almost incompressible
  g
– Assumed to be imcompressible to make
analysis easier
• Specific Weight, 
 kg    kg   m 
 m  s   m   s 
2
2
3
– Weight per unit volume
© 2006 Baylor University
Slide 7
2
Pressure Transducer: Manometer
• How do we measure pressure, p ?
– Change in elevation of a liquid is equivalent to a change in
pressure
• Therefore, a static column of liquid can be used to measure pressure
difference between 2 points
p2  p1   ( z1  z2 )
(White, 1994)
© 2006 Baylor University
Slide 8
Pressure Transducer: Manometer
• Manometer units are in·H2O
– How do I convert in·H2O to more standard units for pressure?
SI Units
English
1 in  H O  249.09 Pa( Pascal )
2

lb
0.036126
in
2
N ( Newton)
1 Pa  1
m
kg  m
1N 1
s
2
2
© 2006 Baylor University
Slide 9
Pressure – Velocity Relationship
F  pA
1
1
2 A
1
F pA
2
2
y
v = Flow velocity
x
F  ma
a
ds
F F F
net
1
2
dv v

dt t
m  Ads  Avdt
© 2006 Baylor University
Slide 10
Pressure – Velocity Relationship
2A
1
v = Flow velocity
ds
dv
p A p A  m
dt
1
( p  p )   v dv
V2
1
2
V1
2
dv
( p  p ) A  Avdt
dt
1
2
© 2006 Baylor University
V V 

( p  p )    
2
 2
2
2
1
2
1
2
Slide 11
Pitot-Static Tube
v
Static Point
s
Static Pressure, (pS )
Static Velocity, (vS)
p
v 0
0
Stagnation Point
p
S
0
Stagnation Pressure, (p0 )
Stagnation Velocity, (v0)
Differential Pressure Transducer
(Manometer)
© 2006 Baylor University
Slide 12
Pitot-Static Tubes
• ps = Static pressure (in the moving
stream)
– Nominal air pressure in atmosphere
• p0 = Stagnation pressure
– Air pressure in the pitot tube
• vs = Static velocity
 2( p0  ps ) 
vs  




– Speed of air passing the pitot tube
• Equivalent to speed of plane through the
air
• v0 = Stagnation velocity = 0
© 2006 Baylor University
Slide 13
1
2
Pitot-Static Tube Sample
Problem
Find :
v
Solution :
 249.09 Pa 

p  p  1.2in  H O
 1in  H O 
S
0
S
2
p  p  298.9 Pa
0
Given :
 air  1.2
kg
m3
2
S

 kg
 2(298.9 Pa)  m  s
v 

kg  Pa
 1.2 2

m

2
s
R'  1.2in  H O
2
3





1
2
1
2
m
m

v  498.2   22.3
s 
s

2
s
© 2006 Baylor University
2
Slide 14
Velocity
• When there is friction between the
fluid and the solid surface
– No slip of the fluid at the
boundary
• Velocity = 0
– A boundary layer forms near the
solid surface
• Shear stress is greatest adjacent
to the boundary layer at the
surface
(White, 1994)
© 2006 Baylor University
Slide 15
Laminar vs. Turbulent Flow
• Laminar -> smooth and steady.
• Turbulent -> fluctuating and agitated.
© 2006 Baylor University
Slide 16
Reynolds Number
• Dimensionless parameter
VL
Re 

– Correlates viscous behavior of all newtonian fluids
–  = density
–  = viscosity
– V = characteristic velocity of flow
– L = length scale of flow
• Most important parameter in fluid mechanics
– Governs transition from laminar to turbulent flow
© 2006 Baylor University
Slide 17
This Concludes Lecture 8
© 2006 Baylor University
Slide 18