Error Using Solve Function

Hello there,

I'm getting an error using the solve function. What is the reason for this and how do we correct it? See below.

Q = 5; s_0 = 0.005; n = 0.02; L = 35; k_e = 0.5; C_D = 0.65; H = 4; g = 9.81;
syms D deltaH
A = pi*D^2/4;
V = Q/A;
R_H = D/4;
eqn1 = deltaH == H - D + L*s_0;
eqn2 = deltaH == (k_e + 2*g*n^2*L/R_H^(4/3) + 1)*(Q^2/(2*g*A^2));
deltaH = double(solve(eqn1 == eqn2, D,"Real",true))

Thanks very much,

Brian

[darova]

It's too complicated. Try vpasolve or fsolve

[Brian Robinson]

Ok so lets use vpa solve:

How would I specify that the solution for D must be less than H/1.2 = 3.33?

So far I have the below code which gives a nonsense solution and I believe there could be more solutions which aren't being shown.

Q = 5; s_0 = 0.005; n = 0.02; L = 35; k_e = 0.5; C_D = 0.65; H = 4; g = 9.81;
syms D deltaH
A = pi*D^2/4;
V = Q/A
R_H = D/4;
eqn1 = deltaH == H - D + L*s_0
eqn2 = deltaH == (k_e + (2*g*n^2*L)/(R_H^(4/3)) + 1)*((Q^2)/(2*g*A^2))
[deltaH, D] = vpasolve(eqn1 == eqn2, deltaH, D);

Thanks again,

Brian

[darova]

try initial guess

[Brian Robinson]

No that didn't seem to make a difference.

[darova]

Makes difference for me

deltaH =
4.1628911435565798210779440646728
D =
10.0

[Brian Robinson]

When I try it I get deltaH = 10 and D = 4.138. Which is the same answer as I got with no parameter.

Regardless, I want to get the other solution which is 1 < D < 2. I can see this solution when I graph the two equations.

[darova]

What about this

[deltaH, D] = vpasolve(eqn1 == eqn2, [deltaH, D],[2 1])
deltaH =
1.1885695516004419959725632337124
D =
2.0

[deltaH, D] = vpasolve(eqn1 == eqn2, [deltaH, D],[2 4])
deltaH =
4.1628911435565798210779440646728
D =
2.0