Sound synthesis of a pipe coupled with a reed requires to finely tune the physical parameters of the underlying model. Although the pipe geometry is often well known, the 1 degree of freedom reed model's parameters are effective coefficients (mass, section, etc) and are difficult to assess. Studies of this coupled system have essentially focused on models without the reed induced flow, and have exhibited two dimensionless parameters γ and ζ, which respectively describe the ratio between feeding pressure and closing reed pressure, and a dimensionless opening of the reed at rest. Including the reed flow in the model, then performing a scaling of the equations, leads to a new third dimensionless quantity that we will call κ. Varying the reed frequency with constant (γ, ζ, κ) on different pipe dimensions shows a certain stability of the model once put under this form. Using a real-time sound synthesis tool, the parameter space (γ, ζ, κ) is explored while the damping of the reed is also varied.