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This report is intended to identify the necessary analytical tools to enable making value judgments for minimizing the various errors typically encountered in capacitance systems. Thus, in addition to identification of error sources, it describes the basic factors which cause the errors. When coupled with appraisals of the relative costs of minimizing the errors, this knowledge will furnish a tool with which to optimize gauging system accuracy, and thus, to obtain the optimum overall system within the constraints imposed by both design and budgetary considerations. Since the subject of capacitance accuracy is quite complex, no attempt is made herein to present a fully-comprehensive evaluation of all factors affecting gauging system accuracy. Rather, the major contributors to gauging system inaccuracy are discussed and emphasis is given to simplicity and clarity, somewhat at the expense of completeness. An overview of Capacitive Fuel Gauging operation is provided in the Appendix.

Thermodynamics of Incompressible and Compressible Fluid Flow

The fluid flow treated in this section is isothermal, subsonic, and incompressible. The effects of heat addition, work on the fluid, variation in sonic velocity, and changes in elevation are neglected. An incompressible fluid is one in which a change in pressure causes no resulting change in fluid density. The assumption that liquids are incompressible introduces no appreciable error in calculations, but the assumption that a gas is incompressible introduces an error of a magnitude that is dependent on the fluid velocity and on the loss coefficient of the particular duct section or piece of equipment. Fig. 1A-1 shows the error in pressure drop resulting from assuming that air is incompressible. With reasonably small loss coefficients and the accuracy that is usually required in most calculations, compressible fluids may be treated as incompressible for velocities less than Mach 0.2.