FV2204

Task 1.

HRH King of Zamunda gathered gruesome data on deaths of his people from fire accidents in the last N=2000 years and put them into two columns in file Zamunda.txt: the year is in the first column and the number of dead that year mi is in the second one. Using Scilab he managed to calculate the average number of casualties per year and the standard deviation from that average l. Then, he approximated the data with the normal distribution curve , which predicts that next year n people will die from fires with probability p(n). Plot the graph of vs , add proper titles and legends. What is the probability that more than 50 people will die in Zamunda from fires next year? Note, inclusion of the script is not required, just the graph, value of p(n>50), and explanations.
[15 marks]

Task 2.

The growth stage of a fire is described by the power law , where , time is in seconds and heat release is in kW. The steady stage starts at , when . It lasts for seconds remaining most of the time close to , but peaks up to at according to the formula . After the steady stage, at time instance , the fire decay stage begins, during which the heat is released according to the formula with . The decay lasts until when . Develop a script to plot the graph of the fire curve as vs which uses if-else and for-cycle constructions according to the exercises in the tutorial. Provide comments to every line of the script. Include the script in the assignment report. Add proper titles and legends. Investigate effect of the coefficient by supplying graphs for three of its different values, e.g. , 0.011, 0.0005. All three graphs should be placed into a single picture in order to get the full mark.
[20 marks]

Task 3.

Develop a Scilab script to calculate the volumetric flux of smoke in a plume produced by a fire of given HRR Q ̇. The plume loses α percent of its heat by radiation and β percent by other means. Carry out calculations for Q ̇=1 MW, α=38%, β=14% and for at least 5 values of height z, e.g. 1, 2, 4, 6, 8, 11, and 15 m. Use appropriate formula for the volumetric flux of smoke from the FPETool manual (page 49). Plot a graph using Scilab script and include it in the report together with the script and explanations.
[30 marks]

Task 4.

Using data from Zamunda.txt, (see Task 1) calculate on how many occasions exactly n people died per year, for n=1,2,…,200. For example, if exactly 30 people died in years 37, 518, 988, 1711, 2001, then , etc. Plot the graph of vs n alongside with the graph of p(n) vs n, add proper titles and legends. Include the graph, the script and explanations of how it works in the assignment report.
[35 marks]