The Problem of Pneumatic Pressure Lag: Part 1—Steady-State Flow in a Tubing System

Abstract

An analytical and experimental investigation of the steady-state isothermal flow in a series system, comprised of a constant-diameter tube with reduced size unions located at the tube extremities, is reported herein. The pressure drop across the system has been determined experimentally as a function of the system geometry. The parameters chosen for investigation were the tube length to diameter ratio L/D, the union diameter to tube diameter ratio Df /D, and the Reynolds number. The ranges of the parameters investigated consisted of 159 ≤ L/D ≤ 1475, 0.7 ≤ Df /D ≤ 1.0, and 200 ≤ Reynolds number ≤ 100,000. All tests were conducted at room temperature. The theory is derived considering each geometric element of the system, such as inlet, development length, exit, and so on, and a set of five simultaneous algebraic flow equations results. Solutions to these were obtained by use of a digital computer. A pseudo-friction factor, for fully developed laminar or turbulent flow, is defined. The result indicates that the correlation of theory with experiment is quantitative over the range of parameters investigated.