1. Lecture #19: Fluid Dynamics I
7 fundamental concepts of fluid mechanics
1. dynamic viscosity
Area = S L
velocity, U
force ~ S x U x L
force
force = m S x U x L,
where m = viscosity (dynamic viscosity)
Fundamental units: M / LT
SI unit: Pascal-second cgs unit: Poise

2. 2. density 3. kinematic viscosity n = density, r = mass / volume
Fundamental units: M / L3
3. kinematic viscosity
dynamic viscosity
density
n =
Ratio of the fundamental
properties of a fluid
fundamental units: L2 / T
cgs unit: Stokes
Air 18 x x 10-6
Water 1 x x x 10-6
dynamic viscosity
(Pa-s)
kinematic
viscosity
(kg m-3)
density

3. 4. no slip condition (boundary layer)
solid surface
Velocity, u =
u (mean stream flow) o
u = 0
(no slip condition)
boundary
layer
Laminar flow over solid surface
laminar flow through pipe
diffusion
convection

4. uinf d (x) = 0.95 x uinf y flat plate with upstream edge x
Ground effect

5. 5. Law of continuity (conservation of mass)
mass flux = r2 s2u2
mass flux = r1 s1u1
S1U1
s2u2
gravity accelerates
water downward
For incompressible fluid r1 = r2
Thus, s1u1=s2u2
= r2 s2u2
r1 s1u1
by conservation
of mass:

7. lung
right ventricle
body
right ventricle

8. constricting streamlines = higher velocity
flow tank
pump
top view
dye injector
stream line
fish
small fluid volume
constricting streamlines = higher velocity

9. 6. Bernoulli Equation (conservation of energy)
consider flow
in one stream tube:
Apply conservation of energy within tube:
kinetic energy
pressure energy
gravitational energy
divide by volume:
consider two points along tube:

11. u1 _ + u2

12. u 7. Reynolds number two sources of force: viscosity force = m u S / L
2) inertial force
= r u2 S
Force sensor u
length, L S
Ratio = Re (Reynolds number)
= r u L / m = u L / v
Re is a dimensionless number that
captures relative importance of viscous and inertial forces:
Low Re
Hi Re
Force ~ u2
Force ~ u
Flows are reversible
Flows are irreversible

13. Forces proportional to u
Low Reynolds numbers
Forces proportional to u

14. Copepod
Re = 300
Sperm whale Re = 300,000,000
Thrips Re = 30
Tuna Re = 30,000,000
Whale sperm Re =
Duck Re = 300,000
Dragonfly Re = 30,000
Bacterium Re =