A 70 ft3 rigid insulated tank contains air at 14.7 psia and 80 º F. The tank is connected to a supply line through a valve. Air is flowing in the supply line at 75 psia and 80 º F. The valve is opened, and air is allowed to enter the tank until the pressure in the tank reaches the line pressure, at which point the valve is closed. The diameter of the connecting pipe is 1 inch.

Write a computer program to model the pressurization process in the tank. The computer program will calculate the pressure, temperature, mass flowrate into the tank and resident mass during the process. Determine the final temperature, mass of air in the tank and time required to pressurize the tank.

Code:

```
P1=75; % in psi
T1=(80+459.67); %in R
A1=(pi*1)/(4*144); % Area in ft^2
D1=1; % Diameter in inch
P2=(14.7); % in psi
T2=T1; %in R
V2=70; % in ft^3
Cp=0.24; % in Btu/lb-R
Cv=0.17; % in Btu/lb-R
k=1.4;% gamma
Cd=0.6; % is unitless
R=53.33; % in ft-lb/lb/R
rho1=(P1*144)/(R*T1); % density in lb/ft^3
rho2=(P2*144)/(R*T2); % density in lb/ft^3
mass2=(rho2*V2); % mass in lb
g=32.174; % in ft/sec^2
dt=0.01; % change in time intervals
n=1;
m(1)=mass2;
P(1)=P2;
T(1)=T2;
while P2<P1-.01
error=1;
n=n+1;
while error>0.001
%Equations
mdot=A1*sqrt(((2*k)/(k-1))*P1*g*rho1*(P2/P1)^(2/k)*(1-(P2/P1))^(k-1/k));
mass2new=mass2+mdot*dt;
u=(mass2*Cv*T2+mdot*Cp*T1*dt)/mass2new; %energy equation
T2=u/Cv;
P2new=mass2new*R*T2/(V2*144);
error=abs(P2new-P2)/P2;
P2=P2new;
end
mass2=mass2new;
T(n)=T2;
P(n)=P2;
m(n)=mass2new;
t(n)=n*dt;
end
%% Output
fprintf('The final temperature = %7.3f R\n',T2)
fprintf('The mass of air in tank = %7.3f lb\n',mass2new)
fprintf('The time required to pressurize the tank = %7.3f s\n',t(n))
figure(1)
plot(t,T,'g','Linewidth',2)
grid
ylabel('Temperature (R)')
xlabel('Time (s)')
title('Time Vs Temperature')
figure(2)
plot(t,P,'b','Linewidth',2)
grid
xlabel('Time (s)')
ylabel('Pressure (psi)')
title('Time Vs Pressure')
figure(3)
plot(t,m,'r','Linewidth',2)
grid
xlabel('Time (s)')
ylabel('Mass (lb)')
title('Time Vs Mass')
```