Based on the atmospheric temperature data of the U.S. Standard Atmosphere (shown

Question

Based on the atmospheric temperature data of the U.S. Standard Atmosphere (shown below), compute and plot the pressure variation with elevation (km), using MATLAB. Please note that for some segments of the graph (e.g., when the elevation is between 0-11 km), temperature linearly changes with elevation (with a negative or positive slope, ), while for some other segments (e.g when the elevation is between 11-20.1 km), the temperature is constant (isothermal). Remember to convert all temperatures from °C to K. Given information: patm-101 kPa; R-286.9 J/kg.K:- 999 kg/m 90 80.0 km 80 70 61.6 km 60 52.4 km 47.3 km 50 a 40 2.2 km 30 20 20.1 km 11.0 km 10 -120-100 -80-60-40-20 20 Temperature (°C)

Explanation / Answer

Ans:

Script.m

h = 0:100:90*1000;

for i=1:size(h,2)

TT(i) = air_pressure(h(i));

end

plot(TT,h)

Constants.m

a1=(-56.5-15.0)/(11000-0);

a2=(-44.5+56.5)/(32.2*1000-20.1*1000);

a3 = (-2.5+44.5)/(47.3*1000-32.2*1000);

a4 = (-20.5+2.5)/(61.6*1000-52.4*1000);

a5 = (-92.5+20.5)/(80*1000-61.6*1000);

g0=9.81;

T_air_seaLevel=288.16;

rho_air_seaLevel=1.225;

P_seaLevel=101000;

R=286.9;

R_earth=6378*1000;

air_temp.m

function [ T ] = air_temp( h1 )

Constants

if h1<=11000 && h1>=0

T=T_air_seaLevel+a1*(h1);

elseif h1>11000 && h1<=20.1*1000

T=air_temp(11000);

return

elseif h1>20.1*1000 && h1<=32.2*1000

T=air_temp(20.1*1000)+a2*(h1-20.1*1000);

return

elseif h1>32.2*1000 && h1<=47.3*1000

T=air_temp(32.2*1000)+a3*(h1-32.2*1000);

return

elseif h1>47.3*1000 && h1<=52.4*1000

T=air_temp(47.3*1000);

return

elseif h1>52.4*1000 && h1<=61.6*1000

T=air_temp(52.4*1000)+a4*(h1-52.4*1000);

return

elseif h1>61.6*1000 && h1<=80.0*1000

T=air_temp(61.6*1000)+a5*(h1-61.6*1000);

return

elseif h1>80.0*1000 && h1<=90*1000

T=air_temp(80.0*1000);

return

else

fprintf("out range ");

T= air_temp(90000);

end

end

air_pressure.m

function [ P ] = air_pressure( h1 )

Constants;

T = air_temp(h1);

rho = air_density(h1);

P=rho*T*R;

end

air_density.m

function [ rho_air ] = air_density( h)

Constants

Ttemp=0;

if h==0

rho_air = rho_air_seaLevel;

return;

elseif h<=11000 && h>0

T = air_temp(h);

rho_air = rho_air_seaLevel*(T/T_air_seaLevel)^(-1*((g0/(a1*R))+1));

return

elseif h>11000 && h<=20.1*1000

Ttemp=air_temp(11000);

rho_air = air_density(11000)*exp((-g0/(R*Ttemp))*(h-11000));

return

elseif h>20.1*1000 && h<=32.2*1000

T = air_temp(h);

Ttemp=air_temp(20.1*1000);

rho_air = air_density(20.1*1000)*(T/Ttemp)^(-1*(g0/(a2*R))+1);

return

elseif h>32.2*1000 && h<=47.3*1000

T = air_temp(h);

Ttemp=air_temp(32.2*1000);

rho_air = air_density(32.2*1000)*(T/Ttemp)^(-1*(g0/(a3*R))+1);

return

elseif h>47.3*1000 && h<=52.4*1000

Ttemp = air_temp(47.3*1000);

rho_air = air_density(47.3*1000)*exp((-g0/(R*Ttemp))*(h-47.3*1000));

elseif h>52.4*1000 && h<=61.6*1000

Ttemp=air_temp(52.4*1000);

T = air_temp(h);

rho_air = air_density(52.4*1000)*(T/Ttemp)^(-1*((g0/(a4*R))+1));

return

elseif h>61.6*1000 && h<=80*1000

Ttemp=air_temp(61.6*1000);

T = air_temp(h);

rho_air = air_density(61.6*1000)*(T/Ttemp)^(-1*((g0/(a5*R))+1));

return

elseif h>80*1000 && h<=90*1000

Ttemp=air_temp(80*1000);

rho_air = air_density(80*1000)*exp((-g0/(R*Ttemp))*(h-80*1000));

return

else

rho_air = 10^-12;

fprintf("out of range ");

end

end

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