task 1hrh king of zamunda gathered gruesome data

Question

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: the year is in the 1^st column and the number of dead that year mi is in the second one. Using Scilab he managed to evaluate 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 shows that next year n people will die from fires with probability p(n). Plot the graph of p(n) vs n, add proper legends and. What is the probability  that more than 50 people will die in Zamunda from fires next year? Note, inclusion of the script is not needed, just the graph, value of p(n>50), and explanations.

Task 2

The growth stage of a fire is explaind by the power law  where 1.9, time t is in seconds and heat release Q'(t) is in kW. The steady stage starts at  t = t_s =  207, when  . It lasts for Τ = 621 seconds remaining most of the time close to Q, but peaks up to Q_s + Q_p = 1358  at t = t_p= 357 according to the this formula  . After the steady stage, at time instance t_d = t_s + Τ, the fire decay stage starts, during which the heat is released according to the formula

with a = 0.02. The decay lasts until t = t_s =1134 when

Prepare a script to plot the graph of the fire curve as Q' vs t which uses if-else and for-cycle constructions according to the exercises in the tutorial. Give comments to every line of the script. Add the script in the assignment report. Add proper titles and legends. Investigate effect of the coefficient b by supplying graphs for three of its distinct values, e.g. b = 0.12, 0.011, 0.0005. All three graphs could be placed into a single picture in order to get the full mark.

Task 3.

Prepare a Scilab script to evaluate 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' = 1MW, 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. Plot a graph using Scilab script and include it in the report together with the script and explanations.

Task 4.

Using data from Zamunda, evaluate on how many occasions v(n) 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 v(30)= 5, etc. Plot the graph of v(n)/N vs n alongside with the graph of p(n) vs n, add proper legends and titles. Add the graph, the script and explanations of how it works in the assignment report.