Download - Lecture 2
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Lecture 2
Properties of FluidsUnits and Dimensions
Engenharia do AmbienteMecânica dos Fluidos Ambiental
• The elemental volume must be much larger than the free random path of a molecule. 2/19
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Density Dimensions and Units
• Dimensions
• Units:
3L
M
Vol
M
SI C.G.S Gravitational (MKpS)
kg m-3 g cm-3 UMM m-3
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Specific Weight, Dimensions and Units
• Dimensions
• Units:
33
2
LF
LMLT
VolMg
g
SI C.G.S Gravitational (MKpS)
N m-3 dine cm-3
(gcms-2)cm-3
(10-3kg*10-2ms-2)(10-2m)-3
dine cm-3
= 10 Nm-2= 1 kgm-2
kg m-3
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Other properties
• Temperature, is a measure of molecule kinetic energy,
• Specific Gravity (dimensionless)
SI C.G.S Gravitational (MKpS)
k k k
12
OH
SG
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Viscosity
When a fluid is sheared, it begins to move at a strain rate inversely proportional to a property called its coefficient of viscosity, .
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Viscosity is responsible for the shear stress which opposes to the relative movement of elemental fluid volumes. Is null if there is no velocity gradient, so it destroys gradients, i.e. generates momentum diffusion.
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Viscosity Units
SI C.G.S Gravitational (MKpS)
N m-2s=kgm-1s-1
(Poiseuille)
dine cm-2s = gcm-1s-1
(Poise=10 Poiseuille)
kg m-2s=kgm-1s-1
1
2
T
FL
dydu
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Kinematic Viscosity
SI C.G.S Gravitational (MKpS)
m2s-1 cm2s-1 m2s-1
121
223
1
23
TLT
LMLT
M
L
T
FL
M
L
12
12
61
55.1
smE
smE
water
air
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Flow between two plates
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Viscosity variability
• Varies much with temperature and weekly with pressure.
• In liquids:– Decreases with temperature,
• In gases:– Increases with temperature.
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No Slip Condition
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Surface Tension
• Exists because intermolecular attraction forces between liquid molecules are higher than between the liquid molecules and air.
• Is responsible for drop formation and for pressure increase inside the drop.
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Spherical droplet
• Surface tension decreases with temperature. This is why solubility increases with temperature.
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Capilarity
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Summary
• We have seen the main fluid properties, their dimensions and units.
• Viscosity is relevant only when there is movement and velocity gradients are present.
• In the next lecture we will see properties of the flow field.
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Velocity, momentum, kinetic energy
dA
dQV
A
QV
L
TL
TL
LL
T
LV
2
13
2
2.
TL
FT
L
MLT
T
L
L
MV
33
2
3
Momentum is the Force applied to a volume multiplied by the action time. A small force acting for long can generate big momentum.
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Dimensions consistency/homogeneity
• In one equation all terms must have the same dimensions.
• In Fluid mechanics this norm is usually respected.
• In many empirical laws (often in natural sciences) it is not, being a source of errors.
• Manning formula for friction is a tricky example of a non-homogeneous formula.
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Other properties computed from velocity
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Momentum and kinetic energy
VVddtVoldtVd
Mdt
Vol
F
• Momentum is often called impulse
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2
2
1
2.
...2
1
VV
dVdV
dtVdt
Vdld
dt
VdldFV
Volume
Work
L
LMLT
T
L
L
MV
3
2
2
2
32
2
1