What does the viscous damping coefficient depend on?

I’m doing a theoretical calculation involving the damping on an oscillating string, and I found the following relationship, where a certain damping factor $$b$$ is proportional to $$\frac{c}{d^2}$$ where $$c$$ is the viscous damping coefficient of the string and $$d$$ is the diameter of the string.

I was wondering, would it be fair to say that this $$b$$ value is proportional to $$\frac{1}{d^2}$$ or is it possible that the viscous damping coefficient could depend on the diameter of the string, therefore making it so that this proportionality isn’t true?

Basically, I’m asking what factors the viscous damping coefficient depends on (mass, surface area, etc), and if any of these factors could in turn depend on the diameter itself?

• The damping coefficient is mostly depend on the oil viscosity – Eli Mar 22 at 13:37

• So would the $1/d^2$ proportionality then be affected by these other forces? Can I say that b is proportional to $1/d^2$? – Jack Ceroni Mar 21 at 21:45
• There isn't necessarily even anything that looks like "b". For example, the standard model of hysteretic damping has the equation of motion (in the frequency domain) as $(k(1 + i \eta) - \omega^2 m)x = f$, not $(k + i \gamma \omega - \omega^2m)x = f$. The hysteretic damping term isn't multiplied by $\omega$, like the viscous damping term. – alephzero Mar 21 at 21:57
• But theoretically, if there was something that looked like b, would it be proportional to $1/d^2$? – Jack Ceroni Mar 21 at 23:13