The dynamic characteristics of cistern manometers are analyzed by the periods and logarithmic decrements of the free oscillation and by the resonance frequencies of the forced oscillation.
The equation of motion of the cistern manometer is given in the form of a second-order nonlinear differential equation that is derived from the Navier-Stokes equation.
The liquid of the manometer used is mercury. The cistern manometers are composed of a mono-tube and cisterns as follows:
diameter of mono-tube:
3, 5, 8mm
diameter of cistern:
3, 13, 20, 30, 44, 77, 106mm
5, 13, 20, 30, 44, 77, 106mm
8, 13, 20, 30, 44, 77, 106mm
The following became clear after the comparison of the experimental values with the theoretical ones.
1. On the periods, experimental values agree well with the theoretical ones. If the diameters of cisterns are more than 30mm, then the values of the period are found to be approximately 1.8sec.
2. When the sizes of the mercurial column and cistern, are increased, the values of the logarithmic decrements increase in proportion.
3. As the sizes of the cisterns increase, the resonance frequency decreases. If the diameters of the cisterns are more than 30mm, the values of the resonance frequencies are found to range from 32 to 34 cycle/min.
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