Is there a way I could assign my variable to a bunch of equations with its value generated on its own ?

Hi there everybody, Im currently doing on my coding right now and encountered on this problem. I would like my variable M2 to generate its own value in which the value satisfies to a bunch of equations that would lead the final equation DeltaP = Patm - P7 = 0. However i wasnt able to achieve such task and would like help on this matter.

R = 287;

T1 = 339;

kc = 1.4;

kc0 = 0.2;

kc1 = 2.498;

kc2 = 3.498;

ktp_volute = 0.9

r1 = 1;

rrms2 = 2;

SW = 0.95;

M1 = rand(1);

for i= 1:length(M1)

%% Ctheta Exit Volute

C1 = M1*(kc*R*T1)^0.5; %absolute velocity inlet

Ctheta_exitvolute = C1*SW*(r1 / rrms2 );

%% Ctheta Inlet Rotor

T02 = 339;

T2 = 332.193;

alpha2 = 70.423;

Rad = deg2rad(alpha2);

%M2 = (M1 * T1^0.5 * SW * r1/rrms2) / T2*0.5 * sin(Rad);

M2 = rand(1);

C2 = M2.*(kc*R*T2).^0.5; %absolute velocity inlet volute

Ctheta2_inletrotor = C2.*sin(Rad);

Delta_Ctheta = Ctheta_exitvolute - Ctheta2_inletrotor;

iter = 0;

maxIter = 0;

%% Delta_Ctheta

while Delta_Ctheta < 0 && iter > maxIter

iter = iter + 1;

Ctheta_exitvolute = C1*SW*(r1 / rrms2 );

Ctheta2_inletrotor = C2.*sin(Rad);

Delta_Ctheta = Ctheta_exitvolute - Ctheta2_inletrotor;

end

if iter == maxIter

warning('Max Iterations reached')

end

end

M6 = rand (1);

M7 = rand(1);

Ktp1 = 1.6775e-12 ;

M2_rel = 0.288;

P01 = 124638.717;

P2 = P01./(((1 + kc0 * M2.^2).^kc2).*(1+ktp_volute)-ktp_volute)

P02_rel = P2.*(1 + kc0 * M2_rel.^2).^kc2;

W2 = 79.468;

W6 = 61.967;

Kpass6 = 0.1;

Kinc1 = 0.522;

Kpass2 = 0.060;

U2 = 207.88944;

U6 = 136.4506;

W6_ideal = sqrt(((W6.^2).* (1+Kpass6)) + ((Kpass2 + Kinc1).* (W2.^2)));

T02_rel = T2.*(1 + kc0 * M2_rel.^2);

T06_rel = T02_rel - kc0./(kc*R) * (U2.^2 - U6.^2);

P06_idrel = P02_rel.* (T06_rel/T02_rel).^kc2;

Wcr2 = sqrt((2 * kc * R * T02_rel)./(kc+1))

Wcr6 = Wcr2.* sqrt(T06_rel/T02_rel)

P6 = (1 - ((W6_ideal./Wcr6).^2).* ((kc-1)./(kc+1))).^(1/kc2).* P06_idrel;

P06 = P6.*((1 + kc0 * M6.^2).^kc2);

for i = 1:length(M7);

P7 = P06 / (((1 + kc0 * M7^2)^kc2) * (1 + Ktp1) - Ktp1)

Patm = 101325;

DeltaP = Patm - P7;

while DeltaP < 0 && iter > maxIter

iter = iter + 1;

P7 = P06 / (((1 + kc0 * M7^2)^kc2) * (1 + Ktp1) - Ktp1);

Delta_P = Patm - P7;

end

if iter == maxIter

warning('Max Iterations reached')

end

end

[Stephen23]

"However i wasnt able to achieve such task and would like help on this matter."

You essentially have two main approaches:

1. if possible solve the equations symbolically/algreabrically, then simply insert the values into the solution.
2. use a numeric optimization routine. In general this requires writing an objective function (containing your "equations") and providing that to the optimization routine. What routine to use depends on the nature of your problem: simple problems in one variable might be solved with FZERO, otherwise you might need to use FMINBND or similar.

See: https://www.mathworks.com/help/matlab/optimization.html

[Danish Iqhwan Rohaizad]

Thank you Stephen for your response. I have edited my coding as per below and would like to ask if its possible for M2 to achieve by using if statement in which the loop would continue on looping until the value M2 obtained ultimately leads Delta_Ctheta2(i) = Ctheta2_exitvolute - NewCtheta2_inletrotor to achieving a value of 0

%% Calculation

%Station 1

R = 287; %Gas constant

T01= 339; %Stagnation Temperature or total inlet temperature

Patm = 101325;

P01 = 124638.717;

A1 = 0.0025686; %Area inlet volute

kc = 1.4; %specific heat ratio

kc0 = 0.2; %specific heat ratio at total state

kc1 = 2.498; %specific heat ratio at inlet volute

kc2 = 3.498; %specific heat ratio at inlet rotor

%Mach Number 1 (Guess)

%M1 =input('What are your M1 value:');% enter the vector M1

M1 = rand(1)

for iter_1 = 1:length(M1)

rho01 = P01./(R*T01); %Stagnation density

rho1 = rho01./(1 + kc0 * M1.^2).^kc1; %flow density inlet volute

T1 = T01./(1 + kc0 * M1.^2); %static temperature inlet volute

P1 = P01./(1 + kc0 *M1.^2).^kc2; %static pressure inlet volute

C1 = M1.*(kc*R*T1).^0.5; %absolute velocity inlet

mdot1 = rho1.*A1.*C1; %mass flow rate inlet volute

end

%% Station 2

%M2 = input('What are your M2 values:');% enter the vector M2

M2 = rand(1)

T02 = 339; %Stagnation temperature or total temperature at rotor inlet

N = 47503; %Rotor speed

omega = (2*pi/60)*N; %Rotor 100% speed angular velocity

ktp_volute= 0.9; %Coeeficient Total Pressure Loss Volute

SW = 0.95; % Swirl Coefficient

B2 = 1; %Inlet rotor blockage factor

r1 = 0.0739; %Inlet volute radius

r2max = 0.047576; %Rotor shroud tip radius at leading edge

r2min = 0.036006; %Rotor hub radius at leading edge

rrms2 = (r2max + r2min)/2; %Average between r2max and r2min

U2 = rrms2 * omega; %Blade speed rotor tip

for iter_2 = 1:length(M2)

Ctheta2_exitvolute = C1.*SW.*(r1 / rrms2 ); %Tangential absolute velocity inlet rotor

P2 = P01./(((1 + kc0 * M2(iter_2).^2).^kc2).*(1+ktp_volute)-ktp_volute); %Static pressure inlet rotor

T2 = T02./(1 + kc0 * M2(iter_2).^2); %static temperature inlet rotor

P02 = P2.*(1 + kc0 * M2(iter_2).^2).^kc2; %Total pressure inlet rotor

rho2 = P2./(R*T2); %Stagnation density

% using continuity equation, mass flow rate inlet rotor = mass flow rate inlet volute

% mdot1 = mdot2

mdot2 = mdot1; %mass flow inlet rotor

leh = 0.018; %rotor leading height

A2 = pi * (r2max +r2min) * leh;%Area Inlet Rotor

%Absolute velocity inlet rotor

alpha2 = (atand((rho2./rho1).*((A2/rrms2)./( A1/r1)).*SW));

Rad = deg2rad(alpha2);

C2 = M2(iter_2).*(kc*R*T2).^0.5; %absolute velocity inlet volute

Ctheta2_inletrotor = C2*sin(Rad);

if Ctheta2_inletrotor < Ctheta2_exitvolute

New_M2 = rand(1);

elseif Ctheta2_inletrotor > Ctheta2_exitvolute

New_M2 = rand(1);

else Ctheta2_inletrotor == Ctheta2_exitvolute

end

New_C2 = New_M2.*(kc*R*T2).^0.5;

NewCtheta2_inletrotor = New_C2*sin(Rad);

Delta_Ctheta2(i) = Ctheta2_exitvolute - NewCtheta2_inletrotor;

end

However, everytime i run this coding I am not able to achieve the value 0 as I intended.

[Torsten]

I already solved this problem in an earlier post:

https://de.mathworks.com/matlabcentral/answers/1679884-generate-random-numbers-to-satisfy-a-variable-on-the-left-and-right-hand-side?s_tid=prof_contriblnk

Was something unclear about the solution ?