## PSN-L Email List Message

Subject: Shape of vane or plunger in liquid damping systems
From: Roger Sparks rsparks@..........
Date: Tue, 08 Feb 2005 16:34:39 -0800

```Hello All,

I am looking for some feedback on my thoughts on liquid damping systems
for amateur seismometers.

All of the liquid damping systems that I have seen use vanes or
plungers.   As a beginning amateur seismologist, I made a vertical
seismometer and used a washer (about 1 1/2 inch in diameter) in liquid
for a damping system.  I adjusted the viscosity of the oil to get an
return overshoot (past center) about as described in several
build-it-yourself sources.

As I gained experience with my instrument, I noticed that I was not
detecting local quakes that I thought I should detect. (I live in
Washington state and we have a lot of local quakes).  From the
literature, I learned that local quakes are higher frequency, so I
guessed that my instrument and amplifier were not detecting or passing
the higher frequency signals.  I easily increased the pass band of the
amplifier, but still very little signal from local quakes.

Then I considered how the plunger of my damping system must be acting as
a low pass filter due to the characteristics of fluid flow at higher
velocities.  I reasoned that the plunger must move a column of fluid at
some velocity.  A fluid moving at a velocity would contain some energy
E = mass * velocity squared and divided by 2.  I further reasoned that
if the frequency doubled, then the distance traveled in a given time
period would also double, and the velocity would also have to double.
If that was correct, then the energy required to set the system into
motion to move a unit distance, would increase by a factor of 4 when the
frequency doubled.  That is a characteristic of a low pass filter system.

I further considered that I was using a large diameter plunger and
expecting  fluid to move from the bottom center of the disk to the top
center each half cycle.  That certainly could not happen at higher
frequencies.  I reasoned that the path length from bottom center to top
center doubled if the  plunger diameter doubled.  A longer path would
require that the fluid velocities would have to be greater if the
displacement was equal for both large and small plungers.  Again, stored
energy in the fluid due to velocity would be energy E = mass * velocity
squared and divided by 2.

I reasoned that the two factors would compound if the frequency doubled.
Thus comparing two dampers, one twice the diameter of the other, the
larger diameter plunger would require 16 times the energy to move at a
doubled frequency through a unit distance compared to the smaller
plunger which only requires 4 times the energy to move through the same
unit distance at the same doubled frequency.

To test my ideas, I drilled several holes in my plunger, thinking that
the center to center distance would drop dramatically.  This occurred,
and I began seeing a much improved response to local quakes.  There was
little change in response to more distance quakes.

If a few holes helped, the ultimate would be to go to a vertical vane
which would consist of thin plates parallel to the direction of intended
motion.  The cross section of the structure at right angles to the
motion would be as small as possible.  The damping then would have to
come from drag or friction as the liquid moved along the smooth sides of
the plates.  From my text books, I noticed that if the flow was laminar,
then the friction would be related only to velocity, not to velocity
squared.  While the flow was laminar, the friction would increase with
frequency in a linear relationship.  At larger movements and very high
frequencies, the flow would be turbulent and the friction again would
become related to the velocity squared.

My parallel vane damper worked very well and now I observe local quakes
frequently.  There is still room for improvement with further reduction
of the structure cross section and more care in making the plates flat
and parallel.

In writing this, I hope that others with a better theoretical knowledge
about fluid flow will critique  my logic for accuracy.  Does a larger
plunger really require 16 times the energy at doubled frequency compared
to 4 times the energy for doubled frequency needed by the smaller (1/2
diameter) plunger? (to move the same displacement)

Wishing all the best,

Roger

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