ChE 540
Viscous Flows
Homework 11
Due 11/24/14
Fall 2014
M. Sahimi
1. Flow Separation in Boundary-Layer Flow
For each of the velocity profiles given below for laminar flow in boundary layers over
a surface, determine whether there is flow separation, or t
ChE 540
Viscous Flows
Homework 7
Due 11/9/2016
Fall 2016
M. Sahimi
1. Exact Solution for Oscillatory Flows with Inertia. I. Flow in an Annulus
As described in class, pulsatile flow, or a oscillatory flow superposed on a steady flow,
occurs when an applied
ChE 540 Homework 2
Due 9/28/17
1
Inclined Plate
Find the velocity profiles for the case where two immiscible liquid falling down an inclined plate.
State all your assumptions.
Figure 1: Inclined plate
1
2
Pressure-driven Flow
Find the velocity profile for
ChE 540 Homework 1
Due 9/12/17
1
Inclined Plate
Find the stress and the velocity profiles for the case where the liquid film is falling on an inclined
plate while the plate is moving with the velocity U . Calculate the film thickness when the net flow
of
ChE 540
Viscous Flows
Homework 6
Due 10/31/2016
Fall 2016
M. Sahimi
1. Laminar Flow in a Channel with Oscillatory Pressure Gradient
Consider fully-developed laminar flow of an incompressible and Newtonian fluid between
two infinite flat surfaces that are
ChE 540
Viscous Flows
Homework 3
Due 9/22/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part I: Radial Mass Flux
Growth of gas bubbles in liquids is an important problem that arises in many contexts,
such as boiling. We consider a small bubble of v
ChE 540
Viscous Flows
Homework 10
Due 11/17/14
Fall 2014
M. Sahimi
1. Use of Lubrication Approximation. Part II: Wire Coating
Consider the last example worked out in class on the application of lubrication approximation, in which the lower surface moves w
ChE 540
Viscous Flows
Homework 2
Due 9/10/14
Fall 2014
M. Sahimi
1. The Del Operator in Cylindrical and Spherical Coordinates, and Vorticity
(a) The three independent variables in cylindrical coordinates are (r, , z) with three unit
vectors (er , e , ez )
ChE 540
Viscous Flows
Homework 6
Due 10/14/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part V: Stress and Rate-of-Strain Tensors
The bubble is still growing, but has not burst yet. So,
(a) Determine the rate-of-strain tensor.
(b) Does the liquid
ChE 540
Viscous Flows
Homework 9
Due 11/10/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part VIII: The Bernoulii Equation
Consider the growing spherical bubble, surrounded by a liquid, studied in the previous
parts of this series.
(a) Determine a
ChE 540
Viscous Flows
Homework 5
Due 10/6/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part III: Relation Between the Pressures in the
Gas and Liquid Phases in Stationary State
As a prelude to Part IV of the problem, consider the spherical gas bub
ChE 540
Viscous Flows
Homework 4
Due 9/29/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part II: Velocity Distribution in the Surrounding
Liquid
Assume that the growing bubble is spherically symmetric about a stationary center.
Derive an expression
ChE 540
Viscous Flows
Homework 1
Due 9/5/14
Fall 2014
M. Sahimi
1. Some Properties of the Curl, or Rotation, Operator
Prove that
(f ) = 0
( v) = 0
(f v) = f v + f v,
where f and v are scalar and vector functions, respectively.
2. The Angle Between Two
ChE 540
Viscous Flows
Homework 7
Due 10/27/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part VI: Viscous Effects
Consider the growing bubble in a surrounding liquid that we have been studying.
(a) Determine the tensor v, where v is the velocity of
ChE 540
Viscous Flows
Homework 12
Due 12/8/14
Fall 2014
M. Sahimi
1. Pressure Distribution in Boundary-Layer Flow over a Flat Surface
A main assumption, backed by scaling analysis that was described in class, is that the
pressure gradient P/y in boundary-
ChE 540
Viscous Flows
Homework 8
Due 11/3/14
Fall 2014
M. Sahimi
1. Dynamics of Bubble Growth. Part VII: Energetics
Consider the growing bubble studied in the previous parts of this series.
(a) Derive an expression for the local rate of viscous dissipatio