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Civil Engineering
University of the Philippines Diliman

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– Second level
• Third level
– Fourth
ESlevel15:
Fluid Mechanics
» Fifth level
Lecture 1
Introduction and Fluid Properties
Prepared by:
Richmark N. Macuha
Assistant Professor

Institute of Civil Engineering, College of Engineering,

1 UP Diliman
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CE 16 Fluid Mechanics II - Villalba
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Outline
I. Fluid Mechanics
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A. Introduction
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B. Fluids vs. Solids
– Second level
C. Fluid as a Continuum
• Third level
D. Units of Measurements
– Fourth level
II. Fluid Properties
» Fifth level
A. Density, Specific Weight, and Specific Gravity
B. Viscosity
C. Bulk Modulus of Elasticity, Surface Tension, and
Vapor Pressure
III. Examples
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Fluid Mechanics
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- the study of effects
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gasses (fluids) which are at rest (static) or in motion
– Second
(dynamic)level
• Third level
Applications
– Fourth level
» Fifth level

Sources of Photos ( from left to right):

- httpwww.nature.orgcsgroupswebcontent@web@lakesriversdocumentsmediailiamna-lake-ak-splash.jpg
- httpsnorthwatch.files.wordpress.com201208sanroque.jpg
- httpsanatate.bzi.ropublicuploadphotos215circulatie_sange_3.jpg
- httpwww.boeingblogs.comrandyimageslightning2.jpg
- httpwww.nationalparks.nsw.gov.au~mediaNPWSImagesParksCoffs-Coast-Regional-
Parkbackgroundsolitary-islands-coastal-walk-hero.ashx

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Units edit Master title style
Measurements
Dimension: a category that represents a physical quantity
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Unit: to edit
a measure of aMaster text styles
specific dimension
– Second level
Unit Systems:
• Third
- SI (System
levelInternationale d’Unites)
- USCS– Fourth
(US Customary
level System)
» Fifth
- Other: BG, EE,level
mks, cgs

Derived Quantities
- force in N (MLT-2)
- energy in J (ML2T-2)
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 Click Fluids
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Solids
Definition of a Fluid
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- any to
substance that deforms
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text styles
subjected to shear stress (gasses and liquids)
– Second level
• Third level
– Fourth level
» Fifth level

Typical Visualization

Solid Liquid
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Mechanics I
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Fluid Master title style
Mass Density, ρ (“rho”)
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- mass
toper unitMaster
edit volume text styles
- unit: kg/m3
– Second level
- common values @ 4oC and 1 atm
• Third level 3
• water, ρ
– Fourth level𝑤𝑎𝑡𝑒𝑟 = 1000 𝑘𝑔/𝑚
» Fifth levelρ𝐻𝑔 = 13590 𝑘𝑔/𝑚3
• mercury,
• air, ρ𝑎𝑖𝑟 = 1.269 𝑘𝑔/𝑚3
- gasses: varies with pressure, temperature, and altitude
- liquids: nearly constant (incompressible) for constant
temperature
Specific Volume: volume per unit mass, 1/ρ
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Fluid Master title style
Specific Weight, γ (“gamma”)
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- weight
to per
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Master
- unit: N/m3
– Second level
𝜸 = ρ𝒈
• Third level
where g is the acceleration due to gravity = 9.81 m/s 2
– Fourth level
» Fifth level
- common values @ 4oC and 1 atm
• water, γ𝑤𝑎𝑡𝑒𝑟 = 9810 𝑁/𝑚3
• mercury, γ𝐻𝑔 = 133.32 𝑘𝑁/𝑚3
• air, γ𝑎𝑖𝑟 = 12. 45 𝑁/𝑚3

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Fluid Master title style
Specific Gravity, SG
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- ratioto
of edit
specific weight of
Master o
a given
text fluid to the specific
styles
weight of water at 4 C (reference specific weight)
– Second level 𝜸𝒇𝒍𝒖𝒊𝒅 𝝆𝒇𝒍𝒖𝒊𝒅
𝑺𝑮 = =
• Third level 𝜸𝒘𝒂𝒕𝒆𝒓 𝝆𝒘𝒂𝒕𝒆𝒓
– Fourth levelquantity
- dimensionless
» Fifth level
- typical values of SG of common fluids:
• water, SG = 1.0
• seawater, SG = 1.03
• mercury, SG = 13.6
• oil, SG ~0.8
• alcohol, SG ~ 0.8
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Viscosity
- measure
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to edit fluid’s resistance to deform when
text styles
subjected to shear stress
– Second level
- absolute or dynamic viscosity: µ (“mu”) in Pa-s
• Third level
- kinematic viscosity: ν (“nu”) in m2/s
– Fourth level
*NOTE: ν = µ 𝝆
» Fifth level

Newton’s Law of Viscosity

𝑑𝑢
τ=µ
𝑑𝑦
Ideal fluid
- incompressible and inviscid Source:

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Fluid Master title style
Bulk Modulus of Elasticity, κ (“kappa”)
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- measure of compressibility
to edit Master textofstyles
a fluid
- relates changes in pressure to changes in volume
– Second level
𝒅𝒑 Δ𝒑
• Third level κ= − = −
𝒅𝑽 𝑽 Δ𝑽 𝑽
where–dp
Fourth
or Δplevel
= change in pressure, in Pa
dV»or
Fifth
ΔVlevel
= change in volume, m3
V = initial volume, m3
- unit: Pa
- important when the fluid is subjected to sudden or
great changes in pressure or when temperature
changes are involved
- for water, κ = 2.2 UPNEC
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Fluid Master title style
Surface Tension, σ (“sigma”)
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- a material
to edit property
Master whereby a liquid at material
text styles
interface exerts a force per unit length along the surface
– Second level
- unit: N/m
• Third level 𝐹σ = σ𝐿
– Fourth level
where Fσ = force due to surface tension, in N
» Fifth level
L = length of surface in contact, in m
Capillary Action
4σ𝑐𝑜𝑠θ
ℎ=
γ𝑑
where h = capillary rise/depression, in m
θ = contact angle, in o
Source:
11 11
d = diameter of the tube,
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httpwww.portageinc.comcommunityppimagesmilk3.jpg

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Fluid Master title style
Vapor Pressure
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- the pressure at which atext
to edit Master liquidstyles
will
vaporize (or boil) at a given
– Second level
temperature
• Third level
- unit:–Pa
Fourth level
- increases withlevel
» Fifth temperature
Cavitation Source (top): httpwww.portageinc.comcommunityppimagesmilk3.jpg
(bottom): httpwww.corvexpumps.comimagescavitation-centrifugal-pumps.jpg

- phenomenon where vapor

bubbles start to form in localized
low-pressure zones of flowing fluids

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Examples
Problem 1
A •cylindrical
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Master text and 90 cm high is filled with
styles
a certain liquid. The tank and the liquid weighed 420 kg and the
weight– of
Second level
the empty tank is 40 kg. What is the specific gravity of
• Third level
the liquid?
– Fourth level
» Fifth level

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Examples
Problem 2
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Determine to pressure increase
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text must be applied to water
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to reduce its volume by 2%.
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• Third level
– Fourth level
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Examples
Problem 3
A •glass capillary
Click tube,
to edit 2-mm intext
Master diameter,
stylesis placed on top of a
mercury layer (SG = 13.6). Calculate the height of the capillary
– Second
depression level The surface tension of mercury is 0.514
for mercury.
N/m and •itsThird level
angle of contact with the glass is 130o.
– Fourth level
» Fifth level

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γ𝑑
 Click to References
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• Streeter, V.L., et al., Fluid Mechanics, 9th ed., McGraw-Hill
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International, 1998
– Second level
• Crowe,• Third
C.T., level
et al., Engineering Fluid Mechanics, 9th ed.,
– Fourth
John Wiley level
& Sons, Inc., 2009
» Fifth level

• Alejandrino, A. A., Lecture Notes in Fluid Mechanics,

National Hydraulic Research Center, 1989

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CE 16CE
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15 Fluid Mechanics
Mechanics
Mechanics I
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