Hello,
I have read your question:

Hello,
I'm currently trying to develop a simple model for a tuning fork gyro.
In calculating the damping as first approximation I used
the couette flow damping. Is there any analytical formula which
expresses the air viscosity as function of the air pressure.
I know that air viscosity is about 1,7/1,8*10-5 Ns/m^2 at ambient
pressure. And at different values like vacuum or something in
the middle?

I have interested to know if you found that formula.
I'm searching an analytical formula to calculate the viscosity of the air at a
pressure about 25 Pa. (0.0036 psi).

Thanks in advance.

Best Regards,
Gabriele Cazzaniga