Fluid Dynamics – Chapter 1: Introduction
Basic Dimmensions
MLT
system
M=mass, L=length, T=time
FLT
system
F=force, L=length, T=time
British Gravitational (BG)
L=foot, T=sec, F=lb
M = slug = lb
⋅
s
2
/ft
(mass = weight/32.2 ft/s
2
)
Temp =
°
F
Abs. Temp =
°
R =
°
F + 460
(Dynamic) Viscosity (
μ
)
:
measures how easily a fluid
flows—relates the shearing
stress and the fluid motion. (
μ
=
slope of shearing stress vs. rate
of shearing strain graph)
Speed of Sound
(for ideal gases)
k = cp/cv (see Tab. 1.7, 1.8)
R=gas const. (see Tab. 1.7,1.8)
T = absolute temperature
General Homogeneous Eqs
:
constants are dimensionless—
equations valid in any system
of units.
Restricted Homogeneous Eqs
:
equations restricted to a
particular system of units.
International System (SI)
L=meter, T=sec, M=kg
F = newton (N) = kg
⋅
m/s
2
Work = J = N
⋅
m
(mass = weight/9.81 m/s
2
)
Temp =
°
C
Abs. Temp = K =
°
C + 273
Sutherland Equation
: empirical
eq. relating viscosity to
temperature for
gasses
For
liquids
, as temperature
increases, viscosity decreases
For
gases
, as temperature
increases, viscosity increases
Bulk Modulus
(measures how
compressible a fluid is)
E
v
=  dp/(d
ρ
/
ρ
)
Quantity
FLT
MLT
Acceleration
L/T
2
L/T
2
Angular velocity1/T
1/T
Angular Accel
1/T
2
1/T
2
Area
L
2
L
2
Density
FT
2
/L
4
M/L
3
Energy/Heat
FL
ML
2
/T
2
Force
F
ML/T
2
Mass
FT
2
/L
M
Mod. of Elas.
F/L
2
M/(LT
2
)
Momentum
FT
ML/T
Power
FL/T
ML
2
/T
3
Pressure/Stress F/L
2
M/(LT
2
)
Temperature
θ
θ
Torque
FL
ML
2
/T
2
Velocity
L/T
L/T
Viscosity(dyn) FT/L
2
M/(LT)
Volume
L
3
L
3
Work
FL
ML
2
/T
2
Density
=
ρ
= mass/volume
Specific volume
=
v
= 1/
ρ
Specific weight
=
γ
=
ρ
g
Specific gravity
= SG
SG =
ρ
/
ρ
H20
(
ρ
= SG
⋅ ρ
H20
)
ρ
H20
=1000kg/m
3
=1.94slugs/ft
3
Weight
=
W
= m g =
ρ
g V
Andrade’s Eq.
(for
liquids
)
Reynolds Number
Re=
ρ
VD/
μ
(unitless)
ρ
= density
V = velocity of flow
D = diameter of pipe
μ
= viscosity
Re<2000 laminar
Re>2000 turbulent
Kinematic viscosity
ν
=
μ
/
ρ
Ideal Gas Law
P =
ρ
R T
P = absolute pressure
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 Fall '07
 Clauss
 Fluid Dynamics, steady flow, Inviscid flow, steady laminar flow, fluid flow velocity, Dynamics Chapter

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