Matlab solving a system of equations

So I have a set of equations listed below. The varying number is the value of x which goes between -0.5 and 0.5 in increments of 0.1. This is then added to 0.153 to give me a vector of values for b. These values need to be then inserted into my equations and solved.

a = 1.4;
x = -0.5:0.1:0.5;
b = 0.153 + x.^2; 

eqn1= Px == dx.*75451.26;
eqn2= dx == (0.183.*578.8.*0.403)/b;
eqn3= Px == dx.*287.*Tx;
eqn4= Tx == 300/(1+0.2.*Mx.^2); 
eqn5= Vx == Mx.*(401.8.*Tx).^0.5;

sol = vpasolve(eqn1,eqn2,eqn3,eqn4,eqn5);

Here are my 5 equations

Answer 1

[Alan Stevens]

Parameters, dx, Px, Tx, Mx and Vx can be evaluated simply as follows:

a = 1.4;
x = -0.5:0.1:0.5;
b = 0.153 + x.^2; 

dx = (0.183.*578.8.*0.403)./b;  
Px = dx.*75451.26;
% Tx = Px./(dx.*287); But this means Tx, Mx and Vx just have constant values:
Tx = 75451.26/287;
Mx = ((300./Tx - 1)*5).^0.5; 
Vx = Mx.*(401.8.*Tx).^0.5;

disp(['Tx = ',num2str(Tx)])
disp(['Mx = ',num2str(Mx)])
disp(['Vx = ',num2str(Vx)])

plot(x,Px,'--o'),grid
xlabel('x'),ylabel('Px')

[Cizzxr]

Apologise i made a mistake in my last message,here are the correct equations;

a = 1.4;

x = -0.5:0.1:0.5;

b = 0.153 + x.^2;

eqn1= Px == 75451.26.*dx.^a;

eqn2= dx == 0.183.*578.8.*(0.403/b);

eqn3= Px == dx.*287.*Tx;

eqn4= Mx == ((-1+(300/Tx))/0.2).^2;

eqn5= Vx == Mx.*(401.8.*Tx).^0.5;

Would this still be done in the same way, as none of them will be constants

[Cizzxr]

Basically, each equation has atleast two unknown that can be solved using the other equations and visa versa

[Cizzxr]

The only value i need to know is Mx also

[Alan Stevens]

With these revised equations the values of Tx, Mx and Vx are no longer constant, but the same general approach can be taken:

a = 1.4;
x = -0.5:0.1:0.5;
b = 0.153 + x.^2; 

dx = 0.183.*578.8.*0.403./b;  
Px = 75451.26*dx.^a;
Tx = Px./(dx.*287); 
Mx = ((300./Tx - 1)*5).^2; 
Vx = Mx.*(401.8.*Tx).^0.5;

plot(x,Mx,'--o'),grid
xlabel('x'),ylabel('Mx')

[Cizzxr]

Im getting an error which is because the variable dx isnt assigned, as shown at the bottom, how can i recify this?

a = 1.4;

x = -0.5:0.1:0.5;

b = 0.153 + x.^2;

Te = 300./(120000./7000).^(0.4./1.4);

density = 7000./(287.*Te) ;

M = ((((120000./7000).^(0.4./1.4))-1)./0.2).^0.5 ;

Ve = M.*((a.*287.*Te).^0.5);

dx = density.*Ve.*(0.403./b)./ Vx;

Px = (7000.*(dx.^a))./(density.^a);

Tx = Px./(287.*dx);

Mx = (((300./Tx)-1)/0.2).^0.5;

Vx = Mx.*((287.*1.4.*Tx).^0.5);

plot(x,Mx,'--o'),grid

xlabel('x'),ylabel('Mx')

>> aeroengines

Unrecognized function or variable 'Vx'.

Error in aeroengines (line 9)

dx = density.*Ve.*(0.403./b)./ Vx;

[Alan Stevens]

With your latest model you can no longer separate the equations - you need an iterative solution. The folowing uses fminsearch. Only you can decide if the resulting values are sensible:

a = 1.4;
x = -0.5:0.05:0.5;
b0 = 0.153; 
Te = 300./(120000./7000).^(0.4./1.4);
density = 7000./(287.*Te) ;
M = ((((120000./7000).^(0.4./1.4))-1)./0.2).^0.5 ;
Ve = M.*((a.*287.*Te).^0.5);
dx0 = density.*Ve.*(0.403./b0)./ Ve;
Px0 = (7000.*(dx0.^a))./(density.^a);
Tx0 = Px0./(287.*dx0);
Mx0 = (((300./Tx0)-1)/0.2).^0.5; 
Vx0 = Mx0.*((287.*1.4.*Tx0).^0.5);

K0 = [dx0; Px0; Tx0; Mx0; Vx0];  % Initial guesses
K = zeros(5,numel(x));
for i = 1:numel(x)
K(:,i) = fminsearch(@(K)fn(K,x(i)),K0);
end
% Extract variables
dx = K(1,:);
Px = K(2,:);
Tx = K(3,:);
Mx = K(4,:);
Vx = K(5,:);

plot(x,Mx,'--o'),grid
xlabel('x'),ylabel('Mx')
axis([min(x) max(x) 0 3])

function F = fn(K,x)
        
        a = 1.4;
        b = 0.153 + x.^2;
        Te = 300./(120000./7000).^(0.4./1.4);
        density = 7000./(287.*Te) ;
        M = ((((120000./7000).^(0.4./1.4))-1)./0.2).^0.5 ;
        Ve = M.*((a.*287.*Te).^0.5);
        
        dx = K(1);
        Px = K(2);
        Tx = K(3);
        Mx = K(4);
        Vx = K(5);
        
        dxn = density.*Ve.*(0.403./b)./ Vx;
        Pxn = (7000.*(dxn.^a))./(density.^a);
        Txn = Pxn./(287.*dxn);
        Mxn = (((300./Txn)-1)/0.2).^0.5; 
        Vxn = Mxn.*((287.*1.4.*Txn).^0.5);
                
        F = norm(dxn-dx)+norm(Pxn-Px)+norm(Txn-Tx)+norm(Mxn-Mx)+norm(Vxn-Vx);

end