Calculate the damping coefficient of air

[a.mlw.walker]

So I am trying to calculate the damping coefficient of air passing around a piston that is oscillating in a tube. The idea is completely theoretical. I don't have any real data.

As far as i understand:

1. The viscous sheer stress = mu.du/dy
2. Therefore the viscous sheer force = (piston surface area)*mu.du/dy

But this is not the damping coefficient. How do I calcualte the damping coefficient?

Alex

 

[minger]

So long as it's completely theoretical...

You could attach the piston to a spring. In the absence of the air, the spring would oscillate forever given an initial displacement. However, with the air, there will be damping. You could measure the displacement of the spring and use something like the log decrement method to calculate the damping coefficient of the system.

 

[jack action]

2. Therefore the viscous sheer force = (piston surface area)*mu.du/dy

But this is not the damping coefficient. How do I calcualte the damping coefficient?

The damping coefficient is the ratio of the force over the velocity (F = C * v). So you already have the force, all you need is the velocity of the piston and divide one by the other to get the damping coefficient.

 

[a.mlw.walker]

The damping coefficient defines the velocity, i want to know the fluid dynamic equations to find the damping coefficient..

 

[alphy]

, to calculate the damping coefficient of air in this scenario, you will need to use a mathematical model or equation that takes into account the variables of the system. This will include the geometry of the piston and tube, the velocity of the piston, and the properties of air such as density and viscosity.

One possible approach is to use the Navier-Stokes equation, which describes the motion of a fluid and includes terms for viscous forces. By solving this equation for the given system, you can obtain the damping coefficient.

Alternatively, you can also use an empirical approach where you conduct experiments with different variables and use regression analysis to determine the damping coefficient. However, this may not be as accurate as using a mathematical model.

It is important to note that without any real data or experimental results, the calculated damping coefficient will be purely theoretical and may not accurately reflect the actual damping in the system. It is always best to validate any theoretical calculations with experimental data.