2M1 Q-stream: EXAMPLE SHEET1 I
1. Partial derivatives
Find the partial derivatives f /x, f /y, 2 f /x2 , 2 f /y 2 and
2 f /(xy) for the following functions:
(a) f (x, y) = x2 2xy + 6x 2y + 1
(b) f (x, y) = exp(xy)
(c) f (x, y) = x2 + y 2 + x2 y + 4
In ea

Hydrodynamics absorption column
(From Coulson and Richardson's Chemical Engineering Volume 6 - Chemical Engineering
Design, 2005)
Packed towers are used for bringing two phases in contact with one another and there will
be strong interaction between the f

The experiment of designing and constructing a pipeline was carried out with a colleague. The aims
of the experiment is to
able to transport the fluid with minimal leakage
keep the design simple and cost efficient
understand the functions and use of vario

Some precautions:
=> Experiments involving poisonous gases like Nitrogen DIOXIDE, Ammonia and Bromine -> Carry out
the exp. in Fume Cupboard or in a well Ventilated Room.
=> Experiments involving heat -> Use a polystyrene cup for insulation to prevent hea

First, some quick tips
Aim to travel light. You're moving into a small room with very limited cupboard space and you'll be moving out again in June. One large suitcase of clothes, a couple of boxes
of other stuff and a binliner of bedding is about the rig

First Block
Group with 4
students per
group
A
Wk 2 Wk/C 3rd Oct
Tues
Thurs
Second Block
B
Wk 3
Tues
C
Wk 4
Thurs
Tues
A (No Labs Wk 6, Reading Week)
Wk 5
Wk 7
Thurs
Tues
Thurs
Tues
B
C
Wk 8
Thurs
Tues
Wk 9
Thurs
Tues
Wk 10
Thurs
Tues
Wk 11
Thurs
Tues
Thur

1. Abstract/summary
Regarding to the experiment objectives, which is to conduct the simple experiments
regarding liquid-liquid extraction and to determine the distribution of coefficient and mass
transfer coefficient with the aqueous phase as the continuo

CHEN 10112T
1 hour and 30 minutes
THE UNIVERSITY OF MANCHESTER
Introduction to Chemical Reaction Engineering
[Date of Examination]
[Time of Examination]
ANSWER ALL QUESTIONS.
Calculators may be used in accordance with the University regulations.
Tables of

School of Chemical Engineering & Analytical
Science
Monday 19th September 2016
Welcome To CEAS
PRESENTATION TOPICS
Introductions
Your Surroundings
Welcome Week & General Info
Working in Partnership Your Voice
Communication
Professor Christopher Harda

Psychometric Tests
A closer
What are they?
Who uses them?
Some specimen questions
Does practising help?
Your questions
Frequently asked questions
Ive been told there will be a test, what is it likely to
be?
Whats negative marking and how do I know

2M1 Q-stream: EXAMPLE SHEET1 II
1. Solution of PDEs by inspection
(a) Show that the function u(x, y) = x y is a solution of the PDE
u u
+
= 0.
x y
(b) Show that u(x, t) = sin(x + t) + cos(x t) is a solution of the 1D
linear wave equation
2u
2u
= 2
x2
t
[H

Lecture Notes for 2M1 Q-Stream
Prof Matthias Heil
School of Mathematics
University of Manchester
M.Heil@maths.man.ac.uk
Course webpage:
http:/www.maths.man.ac.uk/~ mheil/Lectures/2M1
Note:
This part of the course, dealing with functions of two variables

2M1 Q-stream (Matthias Heil, School of Mathematics, Univ. of Manchester)
5
15
Partial dierential equations (PDEs)
Partial dierential equations (PDEs) are functions that relate the value of an unknown
function of multiple variables to its derivatives. In

2M1 Q-stream (Matthias Heil, School of Mathematics, Univ. of Manchester)
5.5
20
Solution of PDEs by separation of variables: Standing waves
One of the most powerful methods for the solution of PDEs is the method of the separation
of variables. Here is a s

2M1 Q-stream: SOLUTIONS
1
II
1. Solution of PDEs by inspection
(a) To verify that the function u(x, y) = x y is a solution of the
PDE
u u
+
= 0.
x y
we form the required partial derivatives
u
=1
x
and
u
= 1,
y
showing that their sum is
u u
+
= 0,
x y
as r

2M1 Q-stream (Matthias Heil, School of Mathematics, Univ. of Manchester)
4
13
Reminder: Ordinary dierential equations (ODEs)
Ordinary dierential equations (ODEs) are equations that relate the value of an unknown
function of a single variable to its deriv

2M1 Q-stream (Matthias Heil, School of Mathematics, Univ. of Manchester)
2
5
Functions of multiple [two] variables
In many applications in science and engineering, a function of interest depends on multiple
variables. For instance, the ideal gas law p = R

Introduction to Chemical Reaction Engineering
Aims:
To introduce and develop an understanding of reaction rate kinetics and the
application of this understanding to the design of a chemical reactor.
Learning Outcomes
By the end of the module the student s