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 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 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
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 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 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 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 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 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 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 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 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