Pressure Tube Modeling Problem

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Abstract

A technique for measuring air pressure at a point on the surface of an airplane's wing involves the use of a long, thin plastic tube, open at one end and dead-ended at the other with a pressure transducer. Many such tubes are attached to the wing with their respective holes located on the surface of the wing. During a flight test, data from the pressure transducer is recorded. However, the desired information is the pressure time history at the open end of the tube. The mathematical formulation of this problem would be: We are given a long thin hollow tube of known geometry with one end open and the other end closed. If the pressure time history is known at the closed end, what are the time histories for the flow rate and pressure at the open end of the tube. A model is presented to describe the flow rate and pressure at the open end and the flow rate at the closed end. This is followed by two different approaches to solve for the pressure time history at the open end of the tube using this model.