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Holly @ 2014 CE
Fundamentals of Fluid
Mechanics
Chapter 1: Introduction
L1.2: Fluid Properties
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Measures of Fluid Mass and Weight
Density (!)1.Mass per unit volume (slugs/ft3; kg/m3)2.Fluid density changes with temperature and
pressure especially for gases3.Specific volume "=1/!(volume per unit mass) Specific Weight (#) weight per unit volume
#=!g (lb/ft3;N/m3)
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Whats the density of water?
! != 1000 kg/m3!!= 1.94 slugs/ft
3
! #= 62.4 lbs/ft3! #= 9800 kg/m3!
SG (water) = 1.0! SG (mercury) = 13.6(But all are slightly temperature-dependent)
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Figure 1.1 (p. 10)Density of water as a function of temperature.
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Measures of Fluid Weight
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Viscosity Fluid Stickiness
Figure 1.2(a) Deformation of material placedbetween two parallel plates. (b) Forces
acting on upper plate.
b
Udt
b
a==!
""#"#tan Rate of Shearing Strain
tt !
!"#
! 0lim$
=!
Therefore,dy
du
b
U
t===
!
!"#!
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Figure 1.3 Behavior of a fluid placed between twoparallel plates.
Shear stress increases with the rate ofshearing strain
dy
duthen !=! "#"
dy
du!
Shear stress between two layers of fluid is proportional to therate of shear strain, that is
viscositydynamicis!dy
du=
DimensionsandUnitsof :FTL!2, lbs / ft
2inBG,Ns /m
2inSI
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Figure 1.6 Linear variation of shearing stress with rateof shearing strain for common fluids.
viscositydynamicis!
dy
du=
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Figure 1.8 Dynamic (absolute) viscosityof some common fluids as a function oftemperature. Why the difference betweenliquids and gases?
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Table 1.5, 1.6, 1.7, 1.8 (front cover)Approximate Physical Properties of Some Common Fluids (BG and SI)
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See Appendix B for Detailed
Temperature Dependencies
Holly @ 2014 CE
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Newtonian vs Non-Newtonian Fluid
Newtonian fluids:the shearing stress is linearly related to the rate of
shear strain, so viscosity is a constant.
Non-Newtonian fluids:the shearing stress is not linearly relating to the
rate of shearing strain; the slope of the shearing stress versus rate of
shearing strain graph is denoted as the apparent viscosity.
Non-Newtonian fluids: thinning fluid, thickening fluid, Bingham plastic,
blood, some slurries, colloidal suspensions, latex paint, quicksand,
Newtonian vs Non-Newtonian Fluid
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Figure 1.7 Variation of shearing stresswith rate of shearing strain for several typesof fluids, including common non-Newtonianfluids.
Newtonian Fluids.
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Fundamental to determining viscous shear stress
Principle: At the molecular scale, a fluid must stick to thesurface with which it is in contact.
Therefore you can always assume that the fluid velocityrelative to the surface at the point of contact is strictly zero.
If you are told or can assume that the velocity profilebetween two surfaces is linear (a special case), then du/dy isa constant and determined by the difference in velocitybetween the two surfaces divided by the gap, or spacing,
between the surfaces.
The No-Slip Condition
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What if velocity profile is not linear?
Then du/dy is not constant, and therefore theshear stress is not constant
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Example 1.5 Newtonian Fluid Shear Stress
Figure 1.5
2
02middle2bottom
2
/4.1412/2.0
)0.2(304.0
00)2
(2
3:middleat the(b)
3)
2(
2
3:bottomat the(a)
)2
(2
3
dy
dustressshear
:Solution
ftlb
h
yV
h
V
h
yV
h
yV
yhy
=!=
=!"=#$
%&'
("!==#$
%&'
("!=
#$
%&'
("!==
="=))
)
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Ideal Gas Law
The density of a gas strongly depends on its pressure and
temperature (unlike liquids)
We use the Ideal Gas Law to relate !, p, and T
!= p / (R T)
R = gas constant, for the particular fluid: F L / (M T)where T is the absolute temperature (Kelvin or Rankine)
(See Tables 1.7, 1.8; R is essentially independent of temperature)
