error in for loop

Hi, I have this error:

Error using mupadengine/feval_internal

More equations than variables is only supported for polynomial systems.

Error in sym/vpasolve (line 172)

sol = eng.feval_internal('symobj::vpasolve',eqns,vars,X0);

My code is the following one.

clear all

clc

syms x

Caudal=[5.93266E-05, 0.00082573, 0.001571951, 0.002318172, 0.003064541, 0.004018053, 0.00493061, 0.005552929, 0.006549172, 0.007338123, 0.008085823, 0.008833522, 0.009415033, 0.009996545, 0.010868442, 0.011574151, 0.012196174, 0.013025341, 0.013895908, 0.014848681, 0.015801455, 0.017251758, 0.018371164, 0.019200479, 0.019781399, 0.02036254, 0.020860957, 0.021234807, 0.021691677]; % m3/s

Presion=[1.638232756, 1.618669688, 1.579773777, 1.540877866, 1.496456555, 1.446449258, 1.379877876, 1.329967516, 1.230219498, 1.141582866, 1.047432951, 0.953283036, 0.881283191, 0.809283346, 0.71509708, 0.643060884, 0.604201324, 0.559755779, 0.515298116, 0.492917821, 0.470537526, 0.420384823, 0.359278257, 0.309307311, 0.259409068, 0.201222724, 0.140297914, 0.093222956, 0.037835664]; %m aire

densidad_aire=1.19; %su densidad a 25ºC en kg/m3

mu=0.0000174;

v_c=mu/densidad_aire; %viscosidad cinemática del aire

E_al=0.502; % rugosidad del disipador

L_disipador=0.045; % ancho disipador 45mm

Largo=0.095; %largo del disipador 95mm ("diametro")

Dist_alabe_alabe=0.002; % 2mm entre cada aleta

Diametro_mojado=(2*Largo*Dist_alabe_alabe)/(Largo+Dist_alabe_alabe);

A_disipador=Largo*Dist_alabe_alabe*45;

V=Caudal/A_disipador;

V_prom=mean(V, 'All')

for M=1:numel(Caudal)

V_Disipador=(Caudal/A_disipador);

Re=(V_Disipador*Diametro_mojado)/(v_c);

%f=vpasolve((1/sqrt(x)==-2*log((E_al/Largo)/3.7+2.51/(Re(M)*sqrt(x)))));

eqn=(1./sqrt(x))==-2.*log((E_al./Largo)./3.7+2.51./(Re.*sqrt(x)));

f=vpasolve(eqn);

h=f*(Largo/Diametro_mojado*V_prom).^2/(2*9.81);

end

Answer 1

[Torsten]

I substituted 1/sqrt(x) by y in your equation. As you can see, there are only negative solutions such that resubstituting gives complex values for x.

clear all
clc
syms y

Caudal=[5.93266E-05, 0.00082573, 0.001571951, 0.002318172, 0.003064541, 0.004018053, 0.00493061, 0.005552929, 0.006549172, 0.007338123, 0.008085823, 0.008833522, 0.009415033, 0.009996545, 0.010868442, 0.011574151, 0.012196174, 0.013025341, 0.013895908, 0.014848681, 0.015801455, 0.017251758, 0.018371164, 0.019200479, 0.019781399, 0.02036254, 0.020860957, 0.021234807, 0.021691677]; % m3/s
Presion=[1.638232756, 1.618669688, 1.579773777, 1.540877866, 1.496456555, 1.446449258, 1.379877876, 1.329967516, 1.230219498, 1.141582866, 1.047432951, 0.953283036, 0.881283191, 0.809283346, 0.71509708, 0.643060884, 0.604201324, 0.559755779, 0.515298116, 0.492917821, 0.470537526, 0.420384823, 0.359278257, 0.309307311, 0.259409068, 0.201222724, 0.140297914, 0.093222956, 0.037835664]; %m aire

densidad_aire=1.19; %su densidad a 25ºC en kg/m3
mu=0.0000174;
v_c=mu/densidad_aire;  %viscosidad cinemática del aire
E_al=0.502; % rugosidad del disipador
L_disipador=0.045; % ancho disipador 45mm
Largo=0.095; %largo del disipador 95mm ("diametro")
Dist_alabe_alabe=0.002;  % 2mm entre cada aleta            
Diametro_mojado=(2*Largo*Dist_alabe_alabe)/(Largo+Dist_alabe_alabe);
A_disipador=Largo*Dist_alabe_alabe*45;
V=Caudal/A_disipador;
V_prom=mean(V, 'All');

for M=1:numel(Caudal)
    V_Disipador=(Caudal(M)/A_disipador);  
    Re=(V_Disipador*Diametro_mojado)/(v_c);
    %f=vpasolve((1/sqrt(x)==-2*log((E_al/Largo)/3.7+2.51/(Re(M)*sqrt(x)))));
    eqn=y==-2.*log(E_al./Largo./3.7+2.51.*y/Re);
    f(M)=vpasolve(eqn);
    if f(M) < 0
      f(M)= 1i/f(M)^2;
    else
      f(M) = 1/f(M)^2;
    end
    h(M)=f(M)*(Largo/Diametro_mojado*V_prom).^2/(2*9.81);
end