Conservation of energy (First law of thermodynamics)
4.
2nd law of thermodynamics
5.
Equation of state
ρ
=
ρ
(p,T)
Unknowns
ρ
,u,v,w,p,T,s
Æ
total number of equations ?

VISCOSITY
Density : measure of the “heaviness” of a fluid.
Viscosity (
μ
) : measure of the “fluidity” of a fluid.
F
orce,
δ
F
x
Velocity,
δ
u
No slip
B
C
A
A’
D
D’
δ
l
δ
y
No slip
y
x
e.g. water & oil approx. have same density but behave differently when flowing
Fluid element at time, t : ABCD
Fluid element at time, t +
δ
t : A’BCD’
δα
•ability of a fluid to flow freely

N
N
direction
plane
that stress
acts
acts
on
y
x
τ
0
lim
x
x
yx
Ay
y
y
F
dF
A
dA
δ
δ
τ
δ
→
=
=
y
A
δ
: area of fluid element in contact with the plate
0
Deformation rate = lim
For small
, tan
t
d
t
dt
l
u t
l
l
y
u t
y
u
d
du
t
y
dt
dy
δ
δα
α
δ
δ
δ δ
δ
δα
δα
δα
δ
δαδ
δ δ
δ
δα
δ
α
δ
δ
→
=
=
≅
=
⇒
=
=
=
⇒
=
Subject to shear stress,
yx
τ
fluid experiences a time rate of deformation (shear rate) as du/dy