Chuck,

Thanks for your comments.  My equations were generated from scratch, 
treating the fluid as moving as a cylindrical mass and the height 
imbalance as the cause of a restoring force, and then I just used the 
spring-mass equations for frequency.  Do you happen to have a copy of 
the RSI paper?

I can see their point, that only a the central portion of the fluid 
moves at full velocity, with a parabolic velocity distribution across 
the tube diameter falling to zero at the wall, though our results 
should at most differ by some percentage.

So I tried it.  Using their formula on the latest FMES design gives a 
1.42Hz natural frequency vs the 1.63Hz I was computing, 15% 
different, which are close enough to what we observe that we probably 
couldn't reliably tell which was closer.  I think that they are 
probably right, and I may want to look into trying to tweak my 
formulas to accommodate a parabolic velocity curve.  I also need to 
see how doing that might affect the frequency corners of the velocity 
response.  I know the formula I am using for the damping does assume 
parabolic velocity so the corners will probably be correct, when 
taken relative to a correct center frequency.

Regards,
Brett

At 01:18 PM 8/1/2011, you wrote:

>All,
>
>I believe there is an error in the FMES spreadsheet just 
>posted.  The correct natural frequency for a "pot and tube" 
>tiltmeter/horizontal seismometer is:
>
>(omega nought)^2 = ((3/2) g)/(2L +l(R^2/r^2)),
>
>where g is acceleration due to gravity, L is height of liquid in the 
>pot, l is length of the tube, R is pot radius and r is tube 
>radius.  The complication is due to non-uniform speed of liquid flow 
>in a tube, maximum at the center, zero in contact with the 
>tube.  Steen and Casey, Theory of the Manometer Accelerometer, Rev 
>Sci Instr, Nov., 1953, p1021-1028.  gives a complete derivation.
>
>Chuck Burch
>__________________________________________________________
>
>Public Seismic Network Mailing List (PSNLIST)
>
>To leave this list email PSNLIST-REQUEST@.............. with the 
>body of the message (first line only): unsubscribe
>See http://www.seismicnet.com/maillist.html for more information.


__________________________________________________________

Public Seismic Network Mailing List (PSNLIST)

To leave this list email PSNLIST-REQUEST@.............. with 
the body of the message (first line only): unsubscribe
See http://www.seismicnet.com/maillist.html for more information.