How to use a solver to get the terminal velocity of a sphere.

Hello Everyone,

I need to know the Terminal Velocity of a sphere falling down in an airstream.

The Problem is, that to find die Drag Coefficient for the Sphere you need to know the Reynoldsnumber. And the Reynoldsnumber is dependable on the velocity of the sphere. I already calculated a solution by hand by guessing some inital values to iterate to the correct Reynoldsnumber. But now i want to use a equation that correlates the Drag Coefficient to the Reynoldsnumber and then use a solver which numerically finds the terminal velocity.

Those are the eqations i want to use:

Can i solve this with the fsolve function?

Best regards!

Answer 1

[Torsten]

v0 = fsolve(@fun,1)

function res = fun(v0)
  d_p =...;
  rho_air = ...;
  nu_air = ...;
  rho_w = ...;
  g = ...;
  Re = d_p*v0*rho_air/nu_air;
  Cd = 24/Re*(1+(Re^(2/3))/6);
  res = v0^2-4*d_p*(rho_w-rho_air)*g/(3*Cd*rho_air);
end

[Niklas Humberg]

Thanks a lot! Is it somehow possible to declare the parameters outside of the function? I need to plott different results against different parameters

[Torsten]

d_p =...;
rho_air = ...;
nu_air = ...;
rho_w = ...;
g = ...;
v0 = fsolve(@(v0)fun(v0,d_p,rho_air,nu_air,rho_w,g),1)
function res = fun(v0,d_p,rho_air,nu_air,rho_w,g))
  Re = d_p*v0*rho_air/nu_air;
  Cd = 24/Re*(1+(Re^(2/3))/6);
  res = v0^2-4*d_p*(rho_w-rho_air)*g/(3*Cd*rho_air);
end