Geoscience Reference
In-Depth Information
1.6 What old saying about snowflakes applies also to turbulent flows?
Explain.
1.7 Explain why most practically important turbulent flows cannot be calculated
numerically through their governing equations.
1.8 Explain how the Reynolds stress emerges when the equation of motion for
turbulent flow is averaged. Interpret the Reynolds stress physically.
1.9 What is a turbulence model? Why are they necessary? What are the two
broad types, and how do they differ?
1.10 Why do you think only the lowest part of the atmosphere is continuously
turbulent?
1.11 Explain the statement “turbulence is an unsolved problem.”
1.12 We say turbulence is
random
and
stochastic.
What do those terms mean?
1.13 Explain how the rate of viscous dissipation can be independent of the fluid
viscosity when that viscosity appears in its definition.
1.14 Explain why the density of a mass-conserving constituent in a turbulent flow
need not be a conserved variable.
1.15 Discuss what properties of the ordinary derivative are shared by the
substantial derivative. What property is not shared?
Problems
1.1
Consider steady, fully developed laminar flow in a circular pipe of diameter
D
. The axial equation of motion is
∂p(x)
∂x
∂
1
ρ
ν
r
∂r
r
∂u(r)
0
=−
+
.
∂r
(a) Why does
p
not depend on
r
?
u
not depend on
x
?
∂p/∂x
not depend
on
x
?
(b) Solve this differential equation for
u(r)
.
(c) Find expressions for
u
ave
,
Eq. (1.2)
, and the Darcy friction factor
f
,
Eq. (1.5)
.
(d) Express the required pumping power per unit mass of fluid in terms of
f
.
1.2
Generalize
Problem 1.1
to include conduction heat transfer in the radial
direction. The temperature equation is
u(r)
∂T(x,r)
∂x
α
r
∂r
r
∂T(x,r)
∂
=
.
∂r
Here
α
=
k/(ρc
p
)
is the thermal diffusivity. Consider the case when
∂T/∂x
does not depend on
x
.
