Theoretical Basis for Fused-Quartz Resonator Flow Tube Design

We have derived the basic equations underlying the design specifications for fused-quartz resonator flow tubes, as well as the equations for the amplitude and angular frequency of the oscillations; developed a design for a resonator detector with a quartz-glass resonator flow tube; and studied the vibrational modes for the quartz tubes in this resonator. We present equations for determining the sensitivity and estimated error of the sensor element in the resonator sensor.