F10ND2/F11ND2/F71NT Numerical Methods for PDEs
1
1.1
Introduction
Denitions
The F10ND2 and F11ND2 modules cover the following topics, Fin MSc students (F71NT) take
just topics 1 and 2:
Section 1. Introduction and basic concepts
Section 2. Parabolic PDEs (
Department of Mechanical Engineering
ME/AA507 Fluid Mechanics
Homework #2, due 020615
Problem 1
Fluid ows between two parallel plates under the eect of a pressure gradient and
the upper plate sliding with respect to the lower one (see gure below). Depen

:
.
The volume flow rate Q between streamlines 1 and 2 can be evaluated by
considering the flow across AB or across BC. For a unit depth, the flow rate across AB
is:
2
2
= 1 = 1

:
Find the stream function associated with the two dimensio
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:
.
:
Find the stream function associated with the two dimensional incompressible flow:
:
Find the path lines for the flow of question 2. Find also equations for the position of a particle along
the path line as a function of time.