Application of the Hydraulic Analogy to Internal Subsonic Flow

摘要

An experimental study was made to determine the quantitative accuracy of the hydraulic analogy when applied to subsonic internal flows such as exist in pure fluid elements. The analogy is based upon the correspondence between density and depth (or pressure and depth squared) when the Mach number and Froude number are equal. Experiments were run in air and in water on geometrically similar nonsymmetrical flow dividers. A factor was used to correct for the difference in apparent specific heat ratios k. (Apparent k = 2 for hydraulic flow, k = 1.4 for air flow.) After this correction was made, the data correlated to within three percent. The Reynolds number for the water flow varied from about 1,500 to 4,000 and, for the air flow, from 17,000 to 100,000. The good correlation, even though some of the water data was taken in apparently laminar flow, indicated that inertial effects predominated over viscous effects. This was because the fluid was essentially at rest before it entered the flow divider. The geometry was characterized by sharp angles and relatively short flow lengths so that convective acceleration and separation zones dominated the flow and established patterns of velocity distribution did not have a chance to completely develop. (Author)