2011 유체역학 Report-4
1.
Figure 1 Show the situation of an incompressible fluid confined
between two parallel, vertical surfaces. One surface, shown to the
left, is stationary, whereas the other is moving upward at a
constant velocity v0. If we consider the fluid Newtonian and the
flow laminar, compute the velocity distribution between the two
parallel, vertical surfaces.
( Hint : the governing equation of motion is the Navier Stokes equation)
Figure 1
2.
An incompressible Newtonian fluid is contained between two long concentric cylinders of
radii λR and R, λ<1. The inner cylinder rotates with an angular velocity Ω. Compute the
velocity distribution between the cylinders and the torque required to hold the outer cylinder
stationary. End effects caused by the finite length of the cylinders may be neglected.
Figure 2 top view and side view of the system
3.
Two immiscible incompressible Newtonian fluids flow concurrently in a plane channel, as
shown in Fig. 3.
a) Determin the velocity distribution.
b) Compute the flow rate of each phase, and compare the flow rate ratio to the in situ
volumetric ratio
Figure 3
4.
서로 다른 점도를 갖는 두 유체가 pipe에 흐를 때, 유체 층에 가해지고 있는 shear stress와
velocity의 분포를 각각 구하고 이를 개략적으로 도시하여 그 특성을 설명하오.
Figure 3
Figure 4
5.
Many two-phase contacting devices require
the flow of a film of liquid over a solid
surface. An incompressible Newtonian liquid
flows under the influence of gravity down an
inclined plane at angle β to the horizontal
( Fig. 5 ). The flow rate per unit width is q.
(a) Compute the velocity distribution in the
film and the film thickness. The liquid
film is in contact with a gas that may be
taken as inviscid.
(Hint : the key to this problem is the
proper formulation of the boundary
condition at the liquid-gas interface.
what is the significance of the fact that
Figure 5
the gas in inviscid?)
(b) Suppose that the liquid film shown in Figure is not isothermal and that the temperaturedependence of the viscosity is not negligible. In particular, assume that
T ( y )  TH  (T0  TH )
0
y
, 
H
1  a(T  T0 )
Where a>0. That is, the temperature profile across the film is linear, and the viscosity
decrease with increasing temperature (as is usual for liquids). Determine
mean velocity, U.
vx ( y ) and
6.
A laminated coating process requires
the
co-current
incompressible
flow
of
Newtonian
two
fluids
down an inclined plane at angle β to
the horizontal ( Fig. 6 ).
Determine the velocity distributions
and layer thicknesses for given flow
rates per unit width qI and qII. (Hint :
what are the boundary conditions?)
Figure 6
7.
A liquid of constant density and viscosity is in a
cylindrical container of radius R and shown in
Figure 7. The container is caused to rotate about
its own axis at an angular velocity Ω. The cylinder
axis is vertical.
of
the
liquid
Find the shape of the free surface
when
steady
state
has
been
established.
Figure 7