Compressible Flow in a Long Tube Closed at One End

Attention is given to pressure variations in a line that terminates at a sensing instrument of negligible volume, constituting a long tube that is closed at one end. An elementary derivation of the response equation that evolves from the laminar flow of a gas moving at subsonic speed is obtained, together with a closed form solution for the limiting case of slowly varying pressure gradients. After the transient phase, the difference in pressures acting at the ends of the duct is proportional to the coefficient of fluid viscosity, the square of the tube length/diameter ratio, and the time rate of change of the applied pressure; it is also inversely proportional to the magnitude of the pressure.