Fluid Dynamics, Calculating viscosity using damping coeffiecient

[goblinhat]

Homework Statement

Hello, I am doing a project which requires damping and have decided to use some viscous damping. It is simply on a hacksaw blade with a weight on the end. Therefore, other than just trial and error I would like to calculate the range of viscosities that may be useful for my damping.

I calcualted the damping coeffiecient c (using the spring coefficient and criticial damping) to be around 2.52. The spring constant being 8N/m and the mass approx 0.2kg. I plan to use a paddle and due to the design it will be around 5cm by 5cm in size and will be located roughly 10 to 15 cm from where it is secured. Also natural frequency is approx 1Hz if that is important.

I was hoping that someone may know some relevant equations to acquire the viscosity needed for critical damping - as i can't find this information anywhere. Any hep including useful links or equations is greatly appreciated.

Homework Equations

c=damping ratio*2*SQRT(km)---

The Attempt at a Solution

N/A

 

[Jhero]

Thank you for sharing your project on damping with us. It sounds like a fascinating project and I am happy to offer some guidance on calculating the range of viscosities that may be useful for your damping system.

Firstly, it is important to note that the damping coefficient c is dependent on both the damping ratio and the square root of the product of the spring constant and the mass. In your case, you have a damping coefficient of 2.52, which means that the damping ratio must be 0.63 (2.52 divided by 4). This is a relatively high damping ratio, which indicates that your system may require a higher viscosity to achieve critical damping.

To calculate the range of viscosities that may be suitable for your project, you can use the following equation:

η = c/(2√km)

Where:
η is the viscosity
c is the damping coefficient
k is the spring constant
m is the mass

Using the values you provided, we can plug them into the equation to get a range of viscosities:

η = 2.52/(2√(8*0.2)) = 1.58 Ns/m^2

This means that any viscosity that falls within the range of 0 to 1.58 Ns/m^2 may be suitable for your damping system. However, keep in mind that this is just a rough estimate and you may need to adjust the viscosity based on other factors such as the size and location of your paddle.

I hope this helps and I wish you all the best with your project. If you need any further assistance, please do not hesitate to ask.