Im trying to solve an equation that have variable on left and right side
9 views (last 30 days)
Show older comments
How do I solve this equation? I'm giving the important information also.
depth= 1385.33
por=0.153
Qv=0.980
B=3200
Rw=0.265
m=1.86
n=2.2
Rt=4.05
Sw=(Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n)
0 Comments
Accepted Answer
John D'Errico
on 23 May 2020
Edited: John D'Errico
on 23 May 2020
How is depth relevant to anything here? It does not appear in the expression. Maybe I'm just not thinking very "deeply" today.
If Sw appears on both sides of the equality, surely you can subtract Sw? Just move everything to the same side. WTP?
por=0.153;
Qv=0.980;
B=3200;
Rw=0.265;
m=1.86;
n=2.2;
Rt=4.05;
fun = @(Sw) Sw - (Rw./((por^m)*Rt*(1+(B*Qv*Rw)./Sw))).^(1/n);
Note that for Sw <= 0, you either have a divide by zero at Sw == 0, or a complex result. So If any real solution exists, it must be for positive Sw.
Also note the use of ./ and .^ where necessary in fun. Does a solution exist? PLOT IT!
fplot(fun,[0,0.01])
yline(0);
It looks like a positive solution exists near 0.007.
[Swsol,fval] = fzero(fun,0.007)
Swsol =
0.00698017018548943
fval =
8.67361737988404e-19
We could also do this using symbolic tools. No analytical solution will exist because of the non-integer power.
syms Sw
vpasolve(fun(Sw))
ans =
0.006980170185489425081287353
No other positive root will exist. That should be not too difficult to prove.
2 Comments
Walter Roberson
on 28 May 2020
If this is a fitting process to determine the optimal Sw, then you would use different code.
You indicate that you have multiple Rt values; for a fitting you would also need multiple values of some other variable -- you need one more more independent variables and one or more dependent variables.
More Answers (3)
Ameer Hamza
on 23 May 2020
Edited: Ameer Hamza
on 23 May 2020
This is one of the methods
syms Sw
depth= 1385.33;
por=0.153;
Qv=0.980;
B=3200;
Rw=0.265;
m=1.86;
n=2.2;
Rt=4.05;
eq = Sw==(Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n);
sol = vpasolve(eq, Sw)
Walter Roberson
on 23 May 2020
depth= 1385.33
por=0.153
Qv=0.980
B=3200
Rw=0.265
m=1.86
n=2.2
Rt=4.05
F = @(Sw) (Sw) - ((Rw/((por^m)*Rt*(1+(B*Qv*Rw)/Sw)))^(1/n));
Sw = fsolve(F, 1.234)
2 Comments
N Sudharshan
on 22 Aug 2023
Edited: Torsten
on 22 Aug 2023
clear all %% solve for SN %%
Z=-1.282;
S=0.5;
PSI=1.9;
M=1000;
W=1000000;
syms SN
eqn = log10(W)==Z*S+9.36*log10(SN+1)-0.20+((log10(PSI/(4.2-1.5)))/(0.40+(1094/(SN+1)^5.19)))+2.32*log10(M)-8.07
solve(eqn)
See Also
Categories
Find more on Calculus in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!