matlab vpasolve function not returning correct answer

hi i have follow code:

clc
clear all
syms yn
b=3;
m=1;
S=0.001;
n=0.014;
Q=28;

A=(b+m*yn)*yn;
T=b+2*m*yn;
P=b+2*yn*sqrt(1+m^2);
R=A/P;
D=A/T;
Eq=Q==(A/n)*S^(0.5)*R^(2/3);
yn=vpasolve(Eq,yn)

matlb give me "yn=- 4.2710 + 2.1157*i " as a Mixed number but the true answer is "yn=2.128"

Why does Matlab say this answer?

Answer 1

[Birdman]

The problem is about initial guess of your equation. vpasolve can not correctly find an initial point and therefore returns a wrong value. My suggestion would be take a look of the graph of the function. First, run the following code:

syms yn
b=3;
m=1;
S=0.001;
n=0.014;
Q=28;
A=(b+m*yn)*yn;
T=b+2*m*yn;
P=b+2*yn*sqrt(1+m^2);
R=A/P;
D=A/T;
fun=Q-(A./n).*S.^(0.5).*R.^(2/3);
plot(-20:0.1:20,subs(fun,yn,-20:0.1:20),-20:0.1:20,subs(fun,yn,-20:0.1:20)==0,'*')

When you check the plot for the input vector and when you zoom in the red line crosses the function, you will see that it crosses when yn has a value of 2.1 or around it. Therefore, you need to set your initial guess argument accordingly, so that you will have an accurate solution. After this step, run the following code and see the result.

yn=vpasolve(fun,yn,3)

I chose 3 as initial point in this situation.

Answer 2

[Torsten]

Use

Eq=Q==(A/n)*S^(0.5)*(R^2)^(1/3);

instead of

Eq=Q==(A/n)*S^(0.5)*R^(2/3);

Best wishes

Torsten.

[mohamad khazaeezade]

this is an Example of hydraulics of my book and yn is normal depth And it is not possible to make a negative number

[mohamad khazaeezade]

yn=2.128 Should be

[Torsten]

And what comes out if you use the other form of the equation ?

[mohamad khazaeezade]

yn become -5.31 , and And that's wrong

[Torsten]

-5.31 is a solution of your equation, but not the one you are looking for.

Setting an initial guess for the solution - like Birdman suggests - should help.

Or you could try to use

assume(yn>0)

Best wishes

Torsten.