How can I solve my for

Hello, I have this error:

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in sym/privsubsasgn (line 1229)

L_tilde2 = builtin('subsasgn',L_tilde,struct('type','()','subs',{varargin}),R_tilde);

Error in sym/subsasgn (line 1060)

C = privsubsasgn(L,R,inds{:});

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]; 
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]; 

v_c=0.0000174/1.19;
A_disipador=0.095*0.002*45;

for M=1:numel(Caudal)
    V_Disipador=(Caudal/A_disipador);  
    Re=(V_Disipador*0.039)/(v_c);
    f(M)=vpasolve((1/sqrt(x)==-2*log((0.502/0.095)/3.7+2.51/(Re(M)*sqrt(x)))))  %HERE IS THE ERROR
    h=f*(0.095/0.0039)*((1.3048).^2/(2*9.81))
end

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in sym/privsubsasgn (line 1168)
L_tilde2 = builtin('subsasgn',L_tilde,struct('type','()','subs',{varargin}),R_tilde);

Error in indexing (line 999)
C = privsubsasgn(L,R,inds{:});

Answer 1

[Walter Roberson]

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]; 

v_c=sym(0.0000174)/sym(1.19);
A_disipador=sym(0.095)*sym(0.002)*sym(45);

for M=1:numel(Caudal)
    V_Disipador=(Caudal(M)/A_disipador);  
    Re=(V_Disipador*sym(0.039))/(v_c);
    eqn = (1/sqrt(x)==-2*log((sym(0.502)/sym(0.095))/sym(3.7)+sym(2.51)/(Re*sqrt(x))))
    f{M} = vpasolve(eqn);  %HERE IS THE ERROR
    h{M} = f{M}*(sym(0.095)/sym(0.0039))*(sym(1.3048).^2/(2*sym(9.81)));
end

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f

f = 1×29 cell array
  Columns 1 through 15

    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

  Columns 16 through 29

    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}    {0×1 sym}

Look at the equation. The constant beign added inside the log() is more than 1, so provided the ratio divided by sqrt(x) is not negative, then the value inside the log() must be greater than 1, so the log must be positive. Positive log multiplied by negative 2 is going to be negative, and if x is positive then sqrt(x) is never negative so 1/sqrt(x) is never negative. We thus conclude that if x is positive then the equation cannot hold.

What if x is negative? Then sqrt(x) would be complex valued and you would be taking log of a complex value and trying to match it to -1i / sqrt(-x) . Can those be equal? I suspect not, but I have not investigated to prove it.