Utilizing MATLAB for Determining Leakage Areas and Ventilation Fan Capacity in Building Structures - Fire Protection Engineering Design.

There are instances where we need to calculate the total mass leakage in a fully sealed building with no exits being used. Traditional methods might involve manual calculations or using Excel, but these can sometimes prove to be less efficient. A more effective alternative could be utilizing MATLAB for this purpose.

Let's consider an example: We have a 15-story building with dimensions of 65 x 65 x 4 meters and doors measuring 0.91 x 2.01 meters each. The door knob has a diameter of about 7.6 mm and both the exterior wall and stairwell leakages are classified as "Loose". Our task is to determine the size of ventilation required for this structure.

By leveraging MATLAB's computational capabilities, we can streamline our calculations and arrive at accurate results more efficiently than traditional hand calculations or Excel-based computations would allow us to do so.

%%%%%%%%%%%%%%%%%%%   Varaiables %%%%%%%%%%%%%
W_building = 75;
L_building = 75;
Stairwell_L = 3;
Stairwell_W = 9;
Floor_height = 4;
N_stories = 15;
Door_W = 0.91;
Door_H = 2.01;
Door_knob = 0.076;
DeltaP_min = 12.4;
Max_Force_opening = 133;
F_door_closing = 20;
T_out = -10; T_out_K = T_out + 273.15;
T_inside = 20; T_inside_K = T_inside + 273.15;
S_leakage = 3.5e-4;
ExteriorWall_leakage = 3.5e-4;
H = N_stories * Floor_height;
Door_leakage = 0.0152;
Roof_leakage = 5.2e-5;
Air_density = 1.2;
C = 0.65;

%%%%%%%%%%%%%%%%%%%Formulas%%%%%%%%%%%%%
Asb = ((Stairwell_W + Stairwell_L)*S_leakage*H)+ N_stories*Door_leakage;
Abo = 0.5 *ExteriorWall_leakage*((((W_building + L_building) - (2*(Stairwell_L+Stairwell_W)))*H) + (2*Door_leakage));
Aso = S_leakage*(Stairwell_W+Stairwell_L)*H;
Roof_total = 2*Door_leakage + (Stairwell_L*Stairwell_W*Roof_leakage);
FT = 3460*((1/T_out_K) - (1/T_inside_K));
FR = 1 + ((Asb/Abo)^2);
Deltap_SBt = ((FT/FR)*H) + DeltaP_min;
DeltaP_Sbt_avg = 0.5*(Deltap_SBt+DeltaP_min);
DeltaP_So = FR*DeltaP_min;
DeltaP_Sot = FR * Deltap_SBt;
DeltaP_So_Avg = 0.5*(DeltaP_So + DeltaP_Sot);
Delta_P_max_allowable = (2*(Max_Force_opening - F_door_closing)*(Door_W - Door_knob))/(Door_W^2 *Door_H);
M_Sb = 0.65*Asb*sqrt(2*Air_density*DeltaP_Sbt_avg);
M_SO = 0.65*Aso*sqrt(2*Air_density*DeltaP_So_Avg);
M_roof = 0.65*Roof_total*sqrt(2*Air_density*(0.5*(DeltaP_Sot + DeltaP_So)));
% Result
M_total = M_roof +M_SO + M_Sb;
Density_outside = Air_density*(T_inside_K/T_out_K);
V_vent_min_req = M_total/Density_outside;


% Therminology ;
% Asb = flow area between the stairwell and the building + Stair door (15 doors)
% Abo = flow area per stairwell between the building and the outdoor + % 2 single % doors on the 1st floor
% Aso = flow area of uniform path between stairwell to the outdoor
% Roof_total = door at stair bottom + roof  Roof access hatch 

For this example, the minimum fan capacity required is 4.1 m^3/s