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1. Classical Mechanics of Fluids (25 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. Please list the Navier-Stokes equations, the equations of energy conservation, and the equation of states. Explain the physical meanings of each term in the energy conservation equations. Are there analytical solutions for these equations? What method can we used to solve the equations for a typical compartment fire?Get help at

[15 marks]

1.2. A pressure meter is calibrated using a Venturi meter attached to a small orifice at the bottom of a water tank. The cross-section areas of the wide and narrow parts of the Venturi meter are of 6 cm2 and 3 cm2 correspondingly. What should be the pressure drop between the wide and narrow parts of the Venturi meter, when the water level in the tank is 8.1 m? Please assume the Venturi meter is installed with pipes of cross-sectional area of 6 cm2 and the pipe finally discharges to open air at the outlet.Get help at
[10 marks]

2. Dimensional analysis (25 marks)

2.1. The Reynolds number is an important number used to distinguish between a laminar flow and a turbulent flow. Please give the formula that is used to calculate the Reynolds number of a pipe flow, explain the meaning of each parameter used in the formula, and then use the dimensional analysis method to demonstrate that the Reynolds number is a non-dimensional?Get help at
[12 marks]

2.2. Kolmogorov scale of velocity in homogeneous turbulence depends on the kinematic viscosity coefficient v [m2/s], specific dissipation rate [J/(kg s)] and, maybe, of fluid density [kg/m3]. Obtain the formula for this dependence using the dimensional analysis.Get help at
[13 marks]

3. Heat Transfer, Thermochemistry and Fluid Dynamics of Combustion (25 marks)Get help at

3.1. Burning of polymethylmethacrylate (PMMA) can be described by the following chemical reaction formula. Get help at

Explain the process of the burning of the PMMA (pyrolysis and reaction with oxygen) and calculate the stoichiometric fuel-air ratio. If 2.0kg of PMM is burnt, how much heat is produced?Get help at
[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. What parameter controls the combustion rate in a typical diffusion flame?Get help at

[10 marks]

4. Characteristics of Flames & Fire Plumes (25 marks)

4.1. Fire plumes are important in fire dynamics. Using a liquid fuel 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.
[15 marks]

4.2 Diffusion flames are common in compartment fires. Assuming a solid fuel is ignited, discuss and analyse factors that affect the spread of the flame on the solid fuel surface. How heat is transferred from the flame to the solid surface?Get help at
[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.Get help at

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
• Single sided
• 1.5 or double line spaced
• Arial 12 point font
• Justified
• Page numbered
• On A4 paper
• Margins left and right 3cm

• Stapled together at the top left-hand corner
• Attached to a cover sheet.

Marks may be deducted for failure to follow these instructions. Please look at the Student Guide to Assessment for more information.





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.Get help at



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