I am very well aware of how to get the damping coefficient experimentally by observing a system in action.
Given the dimensions and fluid properties of a theoretical viscous fluid dashpot, how does one calculate the damping coefficient?
I found this website, which seems to have a calculator that does just that, but I cannot find where they get their formula: http://www.tribology-abc.com/calculators/damper.htm
I want to design an damper with a specific damping coefficient, and would love to be pointed in the right direction.
Best Answer
It seems pretty straightforward how they derived the hidden formula for the damper constant in their idealized design. The volumetric flow rate of fluid displaced by the piston would be $$Q=VA$$where V is the piston velocity and A is the cross sectional area of the piston. This is also the volumetric flow rate of fluid through the small tube of diameter d. The force on the piston is $$F=A\Delta P $$where $\Delta P$ is the pressure difference across the piston. The relationship between the pressure drop and the volumetric flow rate through the small tube is determined by the Hagen Poiseulle equation for laminar flow in a tube: $$\Delta P=\frac{128 QL}{\pi d^4}\mu$$where L is thickness of the piston and $\mu$ is the fluid viscosity. Just combine these equations to get F/V.