Settling times of pressure measurements through capillary tubes
Abstract
A settling time of pressure instrumentation connected through long, thin capillary tubes is studied theoretically and experimentally. A nonlinear partialdifferential equation of heat flow type is derived under an assumption of laminar subsonic isothermal flow for pressure variations along tubes with small radius to length ratios. The equation is integrated numerically for problems with initial stepwise pressure difference assumed to be at the open end of tubes (case A) or at the junction of tubes and pressure transducers (case B); the results are compared with experiments, which show fair agreement as long as the Reynolds number is small. The pressure settling times are shown to depend heavily on the tube radius to length ratio, the tube inside volume to pressure transducer cavity volume ratio, and the absolute value of the pressure to be measured, whereas the dependence on the initial pressure difference across the tube is weak. The existence of a front of pressure variation that travels within tubes is proved and the speed of compression fronts is shown to be smaller than that of expansion ones. The approximate settling time estimation formulas appropriate for very long, thin capillary tubes are presented.
 Publication:

AIAA Journal
 Pub Date:
 October 1979
 DOI:
 10.2514/3.61278
 Bibcode:
 1979AIAAJ..17.1061S
 Keywords:

 Capillary Tubes;
 Isothermal Flow;
 Pressure Measurement;
 Subsonic Flow;
 Tube Heat Exchangers;
 Graphs (Charts);
 Heat Transfer;
 Isothermal Processes;
 Mathematical Models;
 Pressure Distribution;
 Fluid Mechanics and Heat Transfer