Slide 1© 2006 Baylor University

Introduction to Fluid Mechanics

Bellagio Fountain

Slide 2© 2006 Baylor University

Lecture 8Introduction to Fluid Mechanics

Approximate Running Time - 21 minutesDistance Learning / Online Instructional Presentation

Presented byDepartment of Mechanical Engineering

Baylor University

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Slide 3© 2006 Baylor University

Dr. Carolyn SkurlaSpeaking

•Outline– Measuring Devices for

Measuring Drag

– Basics of Fluid Mechanics

– Flight Characteristics of Baseballs & Golf Balls

Lecture 8 Topics

Slide 4© 2006 Baylor University

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

Slide 5© 2006 Baylor University

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

(White, 1994)

Slide 6© 2006 Baylor University

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

Slide 7© 2006 Baylor University

Thermodynamic Properties of a Fluid

• Density,

– Mass per unit volume

• Highly variable in gases (i.e., =f(p))

• Nearly constant in liquids

– Almost incompressible

– Assumed to be imcompressible to make

analysis easier

• Specific Weight,

– Weight per unit volume

g

2322 s

m

m

kg

sm

kg

Slide 8© 2006 Baylor University

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

(White, 1994)

)( 2112 zzpp

Slide 9© 2006 Baylor University

Pressure Transducer: Manometer

• Manometer units are in·H2O

– How do I convert in·H2O to more standard units for pressure?

2

2

22

11

)(11

036126.0)(09.2491

s

mkg N

m

NewtonN Pa

in

lb PascalPa OHin

SI Units English

Slide 10© 2006 Baylor University

Pressure – Velocity Relationship

t

v

dt

dva

x

y

maF ds

A1 2

v = Flow velocity

ApF11

ApF22

21FFF

net

AvdtAdsm

Slide 11© 2006 Baylor University

Pressure – Velocity Relationship

ds

A1 2

v = Flow velocity

dt

dvmApAp

21

dt

dvAvdtApp )(

21

dvvppV

V

2

1

)(21

22)(

2

1

2

2

21

VVpp

Slide 12© 2006 Baylor University

Pitot-Static Tube

Stagnation Point

Stagnation Velocity, (v0)

Stagnation Pressure, (p0 )

0p

00v

Static Point

Static Velocity, (vS)

Static Pressure, (pS )

Sp

sv

Differential Pressure Transducer (Manometer)

Slide 13© 2006 Baylor University

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

– Speed of air passing the pitot tube • Equivalent to speed of plane through the

air

• v0 = Stagnation velocity = 0

2

1

0 )(2

s

s

ppv

Slide 14© 2006 Baylor University

2

1

2

32.1

)9.298(2

Pasm

kg

mkg

Pav

s

2

Pitot-Static Tube Sample Problem

:Given

OHinR2

2.1'

Sv

Find :

OHin

PaOHinpp

S

2

20 1

09.2492.1

PappS

9.2980

:Solution

s

m

s

mv

s3.222.498

2

1

2

2

32.1

m

kgair

Slide 15© 2006 Baylor University

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)

Slide 16© 2006 Baylor University

Laminar vs. Turbulent Flow

• Laminar -> smooth and steady.

• Turbulent -> fluctuating and agitated.

Slide 17© 2006 Baylor University

Reynolds Number

• Dimensionless parameter

– 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

VL

Re

Slide 18© 2006 Baylor University

This Concludes Lecture 8