Linear Fluid Resistance Using Switching Valves and a Tank

Abstract

An active linear fluid resistance is demonstrated using the switched capacitor concept from electronics. For the analogous fluid component, this requires using switching valves to alternately fill and empty a tank. Analysis shows that the equivalent linear resistance is directly proportional to the switching period and inversely proportional to the tank capacitance. For fluid components, the linearity is restricted to those cases where complete filling and emptying is achieved. The time period required to insure linearity is derived in terms of fluid circuit variables. As a result, there is a lower limit on the magnitude of resistance that can be obtained for a given fluid circuit. This magnitude depends on circuit component values, as well as on the desired operating pressure range. However, the net result is that we may construct a linear fluid resistance that has no dependence on orifice sizes, discharge coefficients, or Reynolds number. The experimental fluid circuit contains a source volume in addition to the switching values and tank required for the resistance component. The source volume filters the transients and permits steady state measurements. Experiments are performed for resistances with different switching periods and tank volumes. The experimental resistance values are always within 5 percent of the theoretical predictions. The switched capacitor concept may prove useful in the design of mass flowmeters, frequency-to-analog converters, electric-to-pneumatic transducers, and temperature sensors.