CHEG 544 Transport Phenomena I
Second Hour Exam
Closed Books and Notes
Problem 1). (20 points) The Jeffrey-Hamel Problem. Consider the two-dimensional
problem depicted below. Fluid drains from a trough with interior angle 2 at a rate
Q/W where W is the ex

CHEG 544 Transport Phenomena I
First Hour Exam
Closed Books and Notes
1). (10 points) Using simple arguments based on the linearity of the creeping flow
equations, prove that the drag on a cube under creeping flow conditions is the same
regardless of its

CBE 60544 Transport Phenomena I
Final Exam
Closed Books and Notes
Problem 1). (20 points) Spin coating thick layers. A common way to coat a surface is
to use spin coating, a technique in which a layer of fluid is deposited on a surface (here a
disk of rad

CHEG 544 Transport Phenomena I
Second Hour Exam
Closed Books and Notes
Problem 1). (10 points) Creeping Flow. A pair of identical spheres of radius a and
density !s are settling under the influence of gravity in an infinite fluid of viscosity
and density

CBE 60544 Transport Phenomena I
First Hour Exam
Closed Books and Notes
1). (10 points) Index Notation/Creeping Flow: Prove that the angular velocity of a sphere
freely suspended in pure straining flow (e.g., a linear shear flow with symmetric rate of stra

CBE 60544 Transport Phenomena I
Final Exam
Closed Books and Notes
Problem 1). (20 points) Spin coating thick layers. A common way to coat a surface is
to use spin coating, a technique in which a layer of fluid is deposited on a surface (here a
disk of rad

CBE 60544 Transport Phenomena I
Second Hour Exam
Closed Books and Notes
Problem 1). (15 points) Creeping Flow/Index Notation: Consider a sphere of radius a
undergoing solid body rotation with angular velocity !i in an unbounded fluid at rest.
a. Using ind

CHEG 60544 Transport Phenomena I
First Hour Exam
Closed Books and Notes
1). (15 points) A sphere is freely suspended (e.g., no forces or torques are exerted on it) in an
infinite fluid undergoing the linear shear flow ui = Aij xj at zero Reynolds number.

CBE 60544 Transport Phenomena I
Final Exam
Closed Books and Notes
Problem 1). (20 points) Unidirectional Flows/Scaling Analysis: The Couette viscometer
depicted below is designed such that the velocity of the lower wall is linearly increasing
in time.
u
y

CBE 60544 Transport Phenomena I
Second Hour Exam
Closed Books and Notes
Problem 1). (10 points) Creeping Flow/Index Notation: Consider a sphere of radius a
undergoing solid body rotation with angular velocity !i in an unbounded fluid at rest.
Using index

CBE 60544 Transport Phenomena I
First Hour Exam
Closed Books and Notes
1). (20 points) Consider the flow depicted below. A layer of fluid of thickness h is placed on a
belt, intially moving with a uniform velocity U0 (the belt and the fluid both move with

CBE 60544 Transport Phenomena I
Final Exam
Closed Books and Notes
Problem 1). (10 points) Index Notation: In the Midwest Mechanics lecture a number of
years ago Keith Moffatt gave a fascinating lecture on magneto-electro-hydrodynamic
migration of particle

CHEG 544 Transport Phenomena I
Second Hour Exam
Closed Books and Notes
Problem 1). (10 points) Creeping Flow. A pair of identical spheres of radius a are
settling under the influence of gravity in an infinite fluid as depicted below. At time t=0
they are

CHEG 60544 Transport Phenomena I
First Hour Exam
Closed Books and Notes
1). (20 points) Consider the startup flow depicted below. Fluid is confined in a gap of width
h between a stationary lower wall and a moving upper wall. Initially the fluid is at rest

CBE 60544 Transport Phenomena I
Final Exam
Closed Books and Notes
Problem 1). (10 points) Scaling/Boundary Layers: At high Reynolds number, boundary
layer control is critical! One way of controlling boundary layer growth is via suction essentially sucking

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