Solving system of two (non)-linear eqautions multiple times using a for loop

I want to solve a system of two equations and two unknows (m and A). However. the right side of the second equation is a integer, which I would like to change with every iteration in the for loop. Doing so with every iteration two equations appear and two new unknowns to solve.

The vectors m_dot and A_volute have the solutions, however when I fill in the solutions in the second equation it is not right.

Does anyone know what I am doing wrong?

%% constants
rho = 1.3;
D = 0.126;

%% choose
W = 2600
RPM = 6000
Omega = RPM*((2*pi)/60);

%% solve
m_dot = [];
A_volute = [];

for i = 1500:1000:4500
    syms m A
    E = [(W*rho*A)/(m^2*Omega*D) == 1.2e-8 , m /(rho*Omega*A*D) == i];
    S = solve(E,m,A);

    m_dot = [m_dot, S.m];
    A_volute = [A_volute, S.A];
end

Answer 1

[Star Strider]

I am not certain what the problem is, however putting square brackets [] around the variables you want to solve for may do what you want —

%% constants
rho = 1.3;
D = 0.126;

%% choose
W = 2600

W = 2600

RPM = 6000

RPM = 6000

Omega = RPM*((2*pi)/60);

%% solve
m_dot = [];
A_volute = [];

for i = 1500:1000:4500
    syms m A
    E = [(W*rho*A)/(m^2*Omega*D) == 1.2e-8 , m /(rho*Omega*A*D) == i];
    S = solve(E,[m,A])

    m_dot = [m_dot, S.m]
    A_volute = [A_volute, S.A]
end

S = struct with fields:
    m: 3929008913747544817795072/(17273615680981667385*pi^2)
    A: 75557863725914323419136/(16323566818527675678825*pi^3)

m_dot = 

A_volute = 

S = struct with fields:
    m: 3929008913747544817795072/(28789359468302778975*pi^2)
    A: 75557863725914323419136/(45343241162576876885625*pi^3)

m_dot = 

A_volute = 

S = struct with fields:
    m: 3929008913747544817795072/(40305103255623890565*pi^2)
    A: 75557863725914323419136/(88872752678650678695825*pi^3)

m_dot = 

A_volute = 

S = struct with fields:
    m: 3929008913747544817795072/(51820847042945002155*pi^2)
    A: 75557863725914323419136/(146912101366749081109425*pi^3)

m_dot = 

A_volute = 

Consider using either vpa (results are numerical however remain symbolic) or double (results can be used in code outside the Symbolic Math Toolbox) or both as necessary to rerurn the desired result.

.

[Harm Gilsing]

Thanks, it is working!

[Star Strider]

As always, my pleasure!

Answer 2

[Torsten]

%% constants
rho = 1.3;
D = 0.126;
%% choose
W = 2600;
RPM = 6000;
Omega = RPM*((2*pi)/60);
i = 1500:1000:4500;
%Solutions
m_dot = W./(i*Omega^2*D^2*1.2e-8)

m_dot = 1×4

1.0e+04 * 2.3046 1.3828 0.9877 0.7682

A_volute = W./(i.^2*rho*Omega^3*D^3*1.2e-8)

A_volute = 1×4

0.1493 0.0537 0.0274 0.0166

%Test for solution
(W*rho*A_volute)./(m_dot.^2*Omega*D) - 1.2e-8

ans = 1×4

1.0e-23 * 0 0.1654 0 -0.1654

m_dot./(rho*Omega*A_volute*D) - i

ans = 1×4

1.0e-12 * -0.2274 0 -0.4547 0.9095

[Harm Gilsing]

Thanks, it is working!