MATLAB: How to solve this equation with matlab

solve

clear all;
clc;
data8={'1','10','20','23','12','11'};
kk{1}='Internal pipe roughness (mm)';
kk{2}='Hydraulic diameter of pipe (m)';
kk{3}='Reynolds number ';
kk{4}='Pipe line length (m)';
kk{5}='Average pipe line velosity (m/s)';
kk{6}='Acceleration due to gravity (m/s^2)';
kkk=inputdlg(kk,'Head loss',1,data8);
e11=str2num(kkk{1});
d12=str2num(kkk{2});
re1=str2num(kkk{3});
l2=str2num(kkk{4});
v11=str2num(kkk{5});
g12=str2num(kkk{6});
eqn=(1/sqrt(f9)==(-2*log((e11/3.7*d12)+(2.51/re1*sqrt(f9)))));
solve('eqn','sqrt(f9)');
hf=(f12*l2*(v11^2))/(2*g12*d12);
fprintf('Friction factor in pipe = %f \n  Head loss = %f   (m) \n-----------------------------------------------\n',f1,hf);

Undefined function or variable 'f9'.

Error in Untitled (line 150)

eqn=(1/sqrt(f9)==(-2*log((e11/3.7*d12)+(2.51/re1*sqrt(f9)))));

Best Answer

syms f9 f9sqrt
eqn=(1/sqrt(f9)==(-2*log((e11/3.7*d12)+(2.51/re1*sqrt(f9)))));
F9sqrt = solve(subs(eqn, f9, f9sqrt^2), f9sqrt)

Related Solutions

MATLAB: How to solve this Matrix Equation

The solution is definitely not unique.

Let the two result matrices be [rab11,0;0,rab22] and [rcd11;0;0;rcd22]

Set rcd22 to any non-zero non-infinite value. Then, except for possible singularities,

rab11 = rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))

rab22 = -rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21))

rcd11 = -rcd22*((d11*c11*(b11*b22-b12*b21)*a22-a21*c12*b12*(b11*d21-b21*d11))*a12+a11*a22*b11*c12*(b12*d21-d11*b22))/((c21*d12*(b11*b22-b12*b21)*a22-a21*c22*b12*(b11*d22-b21*d12))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))

You can see in this that rcd22 acts as an arbitrary scale factor for the other coefficients.

The X matrix then becomes

X(1,1) = (b22*a22*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a12*rab21-b21*a22*rab12-b21*a12*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(1,2) = -(b12*a22*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b12*a12*rab21-b11*a22*rab12-b11*a12*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(2,1) = -(b22*a21*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a11*rab21-b21*a21*rab12-b21*a11*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(2,2) = -(b22*a21*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a11*rab21-b21*a21*rab12-b21*a11*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

This was calculated using straight-forward linear algebra by multiplying appropriate inverses on both sides to get two isolated X equations, and then solve()'ing for the corresponding components to be the same.

MATLAB: How to plot a 2D graph while one of the variable is a function of another variable

% note that other values are constant excrpt sigma1, sigma2, a1, and a2; 
for sigma2 = -0.2:0.05:0.2 
a1  = @(a2) sqrt((sigma2*c12*a2-c22*a2^3-sqrt((beta2*k1/2/Rm/ke*E2)^2-...
    (beta2*(K3/Rm+K4*alpha2/Rm/ke)*omega2*a2)^2))/(c32*a2));
a1p = @(a2) sqrt((sigma2*c12*a2-c22*a2^3+sqrt((beta2*k1/2/Rm/ke*E2)^2-...
    (beta2*(K3/Rm+K4*alpha2/Rm/ke)*omega2*a2)^2))/(c32*a2));
sigma1 = @(a2) (c21*(a1(a2))^3+c31*(a1(a2))*a2^2+sqrt((beta1*k1/2/Rm/ke*E1)^2-...
   (beta1*(K3/Rm+K4*alpha1/Rm/ke)*omega1*a1(a2))^2))/c11/a1(a2);
psigma1 = @(a2) (c21*(a1p(a2))^3+c31*(a1p(a2))*a2^2+sqrt((beta1*k1/2/Rm/ke*E1)^2-...
   (beta1*(K3/Rm+K4*alpha1/Rm/ke)*omega1*a1p(a2))^2))/c11/a1p(a2);
sigma1p = @(a2) (c21*(a1(a2))^3+c31*a1(a2)*a2^2-sqrt((beta1*k1/2/Rm/ke*E1)^2-...
   (beta1*(K3/Rm+K4*alpha1/Rm/ke)*omega1*a1(a2))^2))/c11/a1(a2);
psigma1p = @(a2) (c21*(a1p(a2))^3+c31*a1p(a2)*a2^2-sqrt((beta1*k1/2/Rm/ke*E1)^2-...
   (beta1*(K3/Rm+K4*alpha1/Rm/ke)*omega1*a1p(a2))^2))/c11/a1p(a2);
 hold on
 
m = fplot(sigma1,a1,[1e-10,2]); 
m.MeshDensity=1000;
m1 = fplot(psigma1,a1p,[1e-10,2]);
m1.MeshDensity=1000;
m2 = fplot(sigma1p,a1,[1e-10,2]);
m2.MeshDensity=1000;
m3 = fplot(psigma1p,a1p,[1e-10,2]); 
m3.MeshDensity=1000;
  end

Best Answer

Related Solutions

MATLAB: How to solve this Matrix Equation

MATLAB: How to plot a 2D graph while one of the variable is a function of another variable

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