. L 3113
N 11 >393)
k. Ar ._
)V - \0
~ : A \9
\1 . O
(EVA * WV,
KWNE + EV
W 7 a
o kE +\93 O
0 o 0 U
Midterm Examination ChE 630 Transport Phenomena
Professor Dilhan M. Kalyon
October 17, 2002
6:15 pm to 8:30 pm
Open notes and book
1. (20 points) The following velocity distribution, V, describes the flow of a fluid in
a state of pure
Professor Dilhan M. Kalyon
1) Problem 1B.1 from Bird et al. 2nd Edition Page 38
2) Problem 1B.3 from Bird et al. 2nd Edition Page 38
3) Problem 1D.2 from Bird et al. 2nd Edition Page 39
4) Problem 2A.1 from Bird et al. 2nd
Rheol Aeta (2004) 43: 80788
Hansong S. Tang
Dilhan M. Kalyon
Received: 28 March 2003
Accepted: 9 July 2003
Published online: 10 December 2003
H. S. Tang - D. M. Kalyon (Ml)
Stevens 1nstitute of Techno
3B.3 Laminar ow in a square duct
a. The boundary conditions at x = i3 and y = iB are seen to
be satisfied by" direct substitution into Eq. 3B.31. Next we have to see
whether the differential equation
0: (so Z)+#(azvz + 32222)
is satisfied. Substitutin
Flow in a rectangular channel
Effect of the aspect ratio of the channel
How accurate are we to be if we were to assume 1-D flow?
The development of the fully developed flow in the channel
At the entry a flat Vz profile is assumed at 1 m/s.
The flow is iso
E*@- T' SM\.\L \x Ru :4 0\ vusn WC.
)9 \uxNA 5O (61AM) r: (i C 3-3%.agr. lka\avm. , A. .M Q,\,\:'L\ 2
SXMJAQ , WMDAN .
\ I surface\;/
V3 = XL) o 6
xiii/rim END 5FEC<$ ME.
V deG454- _e_ i 2 -A-Z L\)
~93~$ M (mm-66.
Outer cylinder moves with
angular velocity 9
(O u em, 37-10
a) N lame.
u 1A8: \v\_ ,
Cou~\-\4 39.3) ', S*K~I\a 5031.
m- QNED-(avx :
_ \ A /
w - _ Lv i;
1- Ar Ar
Fig. 3.1-1. Fixed volume element Ax Ay
Az through which a uid is owing. The
arrows indicate the mass ux in and out
of the volume at the two shaded faces lo-
cated at x and x + Ax.
3.1 THE EQUATION OF CONTINUITY
This equation i
3A.6 Scale-up of an agitated tank.
The specications for the operation in the large tank (Tank I) are
N1 =2 120 rpm; m = 13.5 cp; p1 = 0.9 g/cm3
and the tank is to be operated with an uncovered liquid surface.
To allow direct prediction of the operation of
Parallel Plate Isothermal flow of a Generalized Newtonian Fluid:
Newtons Law of Viscosity
Consider the flow of fluid occurring between two infinitely long and wide parallel plates
with a distance of separation of H.
Vz ( y ) only
The top plate is
Kinematics is analysis and description of motion. We should first address which
parameters could describe the deformation of the fluid elements.
, the velocity gradient can be shown to be dependent on the
reference frames and thus does not
VECTOR AND TENSOR ANALYSIS
In order to be valid, physical laws should be independent of the coordinate systems
utilized in describing them mathematically. An investigation of the consequences of this
requirement leads to Tensor Analysis.
An nth order tens
WALL SLIP AND BOUNDARY EFFECTS IN
POLYMER SHEAR FLOWS
William Brian Black
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
UNIVERSITY OF WISCONSIN MADISON