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I want to model forces affecting on syringe plunger , but I do not know how to calculate terms like friction and damping coefficient.

What I imagine is that : F_driving = ma + cv + f ----------------(1)

where:

f: friction

c: coefficient of viscous damping

m: mass of plunger (is n't it?)

v and a : velocity and acceleration respectively

In a real setup, I wanted to determine c and f, I used equation (1) to have 2 equations at different F_driving values (by hanging different masses at pluger tip) , and I waited until I reach steady state of speed (i.e. ma=0), so by solving the 2 equations, I got both c and f.

I have several questions in this regard:

1- Is equation 1 is correct? or did I miss any term?

2- Is the approach used to get f and c is correct?

3- I know that friction is not affected by surface area, but how to integrate this rule with the common sense, where you find more resistance in syringe if the pluger is longer or bigger in diameter (i.e surface area is bigger)?

Thanks