I want to program (solve this equation for h) this problem in Matlab but I do not know the appropriate function to use.

I want to program (solve this equation for h) this problem in Matlab but I do not know the appropriate function to use.

h = hss +((((m_Lp/par.rho_L)-(( par.Vp*par.Alpha_Lp_av)))*sin(par.theta))^0.5)*(((((2*pi*hss*(2*par.r_p-hss))^0.5)*1/3))+(1-((1/3)*(2*pi)^0.5))*(h*((2*par.r_p-hss)-h)))

my intent is to calculate for h (h is implicit. h has to be iterated) the other variables are defined:

vp =26.01 m_Lp = 24973 his =0.96 par.Alpha_Lp_av = par theta = pi/180 r_p =0.06 par.ho_L = 1000

Value of h is should be between 0-10

[Torsten]

(2*pi*hss*(2*par.r_p-hss))^0.5 is complex-valued for the parameters given.

Answer 1

[Torsten]

h can be explicitly solved for:

par.Vp = 26.01;
m_Lp = 24973;
hss =0.96;
par.Alpha_Lp_av = pi/180;
par.theta = pi/180;
par.r_p =0.06;
par.rho_L = 1000;
c1 = hss;
c2 = ((m_Lp/par.rho_L- par.Vp*par.Alpha_Lp_av)*sin(par.theta))^0.5;
c3 = (2*pi*hss*(2*par.r_p-hss))^0.5*1/3;
c4 = 1-1/3*(2*pi)^0.5;
c5 = 2*par.r_p-hss;
p = -(c2*c4*c5-1)/(c2*c4);
q = -(c1+c2*c3)/(c2*c4);
h(1) = -p/2 + sqrt((p/2)^2-q)
h(2) = -p/2 - sqrt((p/2)^2-q)

Best wishes

Torsten.

[Stephan]

A more elegant and more exact solution than fsolve

[gbok]

Thank you very much