University of Central Lancashire
School of Engineering
FV2001 Assignment Brief
Assignment Details
Answer ALL questions. The marks for each question are shown in square brackets “[ ]”
next to the question.
1. Classical Mechanics of Fluids (35 marks)
1.1. The Navier-Stokes equations govern fluid flow in fires and fire protection systems. It is
the foundation for water flows, gas flows, and fire simulations and modelling. List the
Navier-Stokes equations, the equation of continuity, the equations of energy conservation,
and the equation of state in differential equation form. [4 marks]. Explain the physical
meanings of each term in the Navier-Stokes equations [3 marks]. Indicate what terms in
the equation need turbulence modelling [1 marks]. Discuss the reasons why turbulence
models are necessary by analysing the scale of vortices in fluid flow and the required
capacity of computers? [6 marks] Give an example of the source term in the equation of
energy conservation [1 mark].
[Total 15 marks]
1.2. A vertical riser of 100mm in diameter is provided to a building to facilitate firefighting.
The inlet of the riser is 1m above ground level. The outlet of the riser is 34m above the
ground level. A hose of 60m in length and 80mm in diameter is connected to the outlet of
the riser and horizontally laid on the floor. The hose has the same height as the riser outlet
and its nozzle is open. Assuming the a fire engine is connected to the inlet of the riser and
maintains a constant flow velocity of 8 m/s at the inlet of the riser, please perform the
following: (1) draw a diagram to show the system; [5 marks] (2) assuming energy loss
along the pipes can be omitted, calculate the pressure at the inlet of the riser using
Bernoulli’s equation and the equation of continuity; [7 marks] (3) assuming the pipe
surface roughness is ε=0.1mm, density of water is 1000kg/m3
, and viscosity μ=0.9×10-3
kg/(m∙s), calculate the pressure and water volume flow rate at the inlet of the riser use the
Swamee-Jain equation for the friction factor; [7 marks] (4) compare the results obtained in
items (2) and (3). [1 marks]
[Total 20 marks]
2. Dimensional analysis (15 marks)
2.1. Find the dimensions of the following term.
( − )

Where ρ is the density, v is the velocity, a and b are lengths, and µ is dynamic viscosity of
the fluid.
[5 marks]
2.2. Kolmogorov scale of velocity
 T
in homogeneous turbulence depends on the
kinematic viscosity coefficient  [m2
/s], specific dissipation rate

[J/(kg s)] and, maybe, of
fluid density

]. Obtain the formula for this dependence using dimensional
analysis method. You should provide each step of your analysis and make appropriate
assumptions where necessary. Only provide the formula or obtain the formula by other
methods are not acceptable and will not be awarded any marks.
[10 marks]
3. Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion (25 marks)
3.1. A steel beam is involved in a compartment fire. Assume the compartment floor is
uniformly covered by wood, a fire is initiated on the wood surface directly under the beam
that is at the centre of the compartment, explain how the fire spreads across the floor,
discuss factors that affect the fire spread, qualitatively analyse how the temperature of the
steel beam changes in the compartment considering the fire growth, flashover, and decay.
[15 marks]
3.2. Define the Reaction Rate of a fire, then, discuss the factors that affect the reaction
rate in a general secondary-order A + B → C + D chemical reaction. In a fire, where does
the chemical reaction happens? Compared with diffusion of oxygen from a higher
concentration area to a low concentration area, how fast is the chemical reaction in a fire?
[10 marks]
4. Characteristics of Flames & Fire Plumes (25 marks)
4.1. Fire plumes are important in fire dynamics. Using a fire at the centre of a compartment
as an example, explain the characteristics of a fire plume and generalise the axisymmetric
plume model for calculating the smoke production rate and temperature along the axis of
the fire plume. [8 marks] Search literatures to find other plume equations and compare
them with the axisymmetric plume model. [7 marks]
[15 marks]
4.2 Diffusion flames are common in compartment fires. Analyse the flame structure of a
diffusion flame; identify the chemical reaction zone; explain how fuels and oxygen are
transported into the reaction zone; how heat and products are transported from the
reaction zone? Compare the flame thickness with the Komogorov length scale.
[10 marks]
Max total mark: 100.
Should any part of the assignment not provide sufficient information, the student should
select her/his own data and explain the choice.
The word limit is 1,500 words (+/-10%). This excludes footnotes but includes quotations.
 You must answer the questions set
 You must keep to the word limit of 1,500 words
 You must demonstrate that you have met the learning outcomes
Presentation Instructions
It is your responsibility to ensure that your work is neatly and accurately presented.
The work must be:
 Word-processed and saved as a pdf file for final submission.
 1.5 or double line spaced
 Justified
 Page numbered
 Named FV2001-Assignment.pdf and submitted online from the Blackboard
 Margins left and right 3cm
 Insert a cover sheet in front.
Marks may be deducted for failure to follow these instructions. Please look at the Student
Guide to Assessment for more information.
The use of work produced for another purpose by you, working alone or with others, must
be acknowledged.
Copying from the works of another person (including Internet sources) constitutes
plagiarism, which is an offence within the University’s regulations. Brief quotations from the
published or unpublished works of another person, suitably attributed, are acceptable. You
must always use your own words except when using properly referenced quotations.
You are advised when taking notes from books or other sources to make notes in your
own words, in a selective and critical way.
Your work must be submitted with:
 Online with a front cover sheet (detailing the module code and title, coursework title,
module name and student name, word count, date submitted).
The assignment should be submitted electronically via Turnitin (a guide to submitting work
via Turnitin can be found on Blackboard).
The deadline for submission is 24.00 on 27th March 2018
Every attempt will be made to ensure that the work will be marked and available for
viewing by 15 April 2018
The assignment is worth 40% of the total module assessment.
Learning outcomes
This assessment will test your ability to meet the learning outcomes as described in your
module booklet, specifically:
1. Describe fundamental principles developed in fluid dynamics, heat and mass transfer
4. Examine the main characteristics of jet and buoyant flames, fire plumes and flows
encountered in fire environments

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