IT and CAD Portfolio - Assignment Example

Contents Contents 1 Question 1: MS Equations 2 Question2: part 1:chart 4 Question2: part 2: IF Function 5 Question 3: maple 6 Question 4 Gimp 7 Question 5: memory estimation 9 Estimation of computational memory 9 References 11 Question 1: MS Equations Eq (11) pg 2-5 :  This is the equation for the normalized flame height In this equation, non-dimensional flame height in regime of momentum depends simply on the mass stoichiometric ratio and density of the source gas at discharge. Transition to the momentum regime, RM should be 0.1 and the height of the flame in the momentum regime has a significant difference Eq (1) pg 2-19 :  For 0.26  2.0 This is the equation for the thickness of a ceiling jet. From Alpert’s theory, the thickness of a ceiling jet ℓT is the distance below a ceiling where excess gas temperature below an ambient value ∆T drops to a value of 1/℮ (1.2718) of the maximum excessive temperature. This equation is a correlation that was developed by Motevalli and Marks from data on temperature and it is a predicted constancy of the ceiling jet thickness. Eq (1) pg 2-5  In the above equation, the symbols represent the following: J = fuel species of interest Cj = volume concentration of fuel j when the fuel stream is stoichiometrically mixed with oxidant stream ∆Hc,j = heat of combustion of the species j (K) TSL, j = adiabatic flame temperature at the stoichiometric limit for fuel species j (K) To = temperature of the gas mixture prior to reaction (K) nprod = number of moles of products complete combustion per mole of reactants (stoichiometric mixture of fuel and oxidant streams) Cp = heat capacity of products of complete combustion (kj/g.mol K) 1.0 is the ignition index which indicates that there is expected ignition if the mixture has sufficient fuel. Question2: part 1:chart This is an explanation for the work done on the excel function labeled Excel1. This is a graph of the functions f1, f2 and f3. For function “F1(x)”, the correspond value for the function has been computed by first putting the range of values given which is “0 to 10” with a precision of 0.1. The values have then been computed using the formula “=5*COS(4*A2)/2*(A2+1”. This formula has then been applied in all the cells in that column For the second function, the formula “=SIN(2*A2)*EXP(-A2/4)”, and F3 by the formula “=3*SIN(A2)*TANH(A2/2)/(A2+1)”. All the formulae are pulled down so that they can be applied in all the cells in the respective columns Question2: part 2: IF Function This is an excel spreadsheet with the IF function. It shows the use of the IF statements to compute a range of excel functions. The “IF” statement has been used in this statement to determine the grades using the logical tests procedures In order to determine the grades, the marks are first computed using the necessary formula. All the formulae in excel are preceded by the equals sign “=”. The formulae which were applied in the question are as follows The CAT marks for the first and the second CATs are given and entered into the respective places The final marks for the CAT was computed by entering the formula “=(D11*0.4+E11*0.6)” in F11 and then applying the same formula to all the cells in the F column. The final exam marks were entered in their respective cells The total marks were computed be entering the formula “=(F11+G11)/2” The IF function has been used to get the grades by using the syntax “=IF(H11>=70,"A",IF(H11>=60,"B",IF(H11>=50,"C",IF(H11>=40,"D","F"))))”. This is a logical test which compares the total marks given in column h11 with the criteria needed to qualify the marks to the given grades Graphs were then plotted using the graph wizards Question 3: maple Function and the derivative Calculating the derivative using maple and plotting the functions In order to calculate the derivative of a function  in maple we first define the function as below: - f := - > (sin(x-2)+x^2)/(sin(x^2)-exp(x))*((1/(x-1))-2x); after defining the function, we differentiate it using the diff command as below diff(f(x), x); to plot the functions, we use the plot command as below plot (f(x), x=0..10); Question 4 Gimp Screen print The first step in drawing a plan for a classroom is to draw the ground floor plan The next step is to draw the walls using differing depths for the inner walls and the outer walls Make sure that all the walls which have been drawn are perpendicular to each other. Considering the diagram at hand, draw the floor plan to a scale representing the 10m by 20m measurements After drawing the wall plan, one should now concentrate on adding the openings that will represent the doors and the windows. To add the openings, start with the door. Make it to be about 3.5m and let it be near one of the long ends. The next step is to make the openings for the windows. After the windows and the doors have been traced, move to another layer on top of the current layer and add the outer profiles On creating a crispy outline, add the window and the door details and any other architectural designs Question 5: memory estimation Estimation of computational memory “Estimate computer memory in bytes and computational time required to carry out a simulation of a 10 minutes fire in a room of size 4m by 5m by 3m. assume that the kolmogorov length scale is 1μm and the length scale of the flame thickness is about 1mm. in every grid point the fire is fully quantified with 100 of physical parameters such as gas velocity, pressure, temperature, concentrations of chemical components, etc. each of these parameter is represented in a computer with a 64 binary digit number, i.e. takes 8 bytes of computer memory, and the computer can do 2.5×〖10〗^15 arithmetic operations per second. The computational time step ∆t corresponds to the CFL condition ∆t=v∆x with the fluid speed v of order 1m/s and 1000 arithmetic operations is needed in order to advance numerical solution per time step per grid node. Here ∆x is the grid cell size. Provide the estimations for 3 approaches: DNS resolving all possible flow features Fine LES on a grid resolving the flame structure Crude LES on a grid with the cell size of 1cm” Volume of the room: - V = 4m*5m*3m = 60m3 The features of the flow are on the Kolmogorov length scale nK = 10-6m The number of the needed cells is of the order N = V/n3K N = 60/10-18 = 6.0 * 1019. Every cell has 100 parameters which need a storage area of 8 bytes. Due to this the solution at every step will require: 100 X 8 X N = 100 X 8 X 6.0 * 1019 = 4.8 X 1022 bytes of memory area In order to advance the numerical operations, this will take 1000 arithmetic operations per grid, to advance the whole system will take M = 1000 X 10 X N = 1000 X 10 X 6.0 X 1019 = 6.0 X 1024 operations References SFPE Handbook of fire protection engineering. 3rd edition.SFPE. 2002. Karlin, V. 2011 Introduction to CFD Read More