Quantitative flow visualization using the hydraulic analogy

Abstract

The current work describes the development of a non-intrusive optical method for the quantitative determination of water heights along a hydraulic jump in shooting water flows on a water table. The technique involves optically superimposing a series of alternating dark and clear fringes on the water flow. It is proposed that the fringe deviations seen under a hydraulic jump can be simulated using a series of optical prisms oriented along the direction of the hydraulic jump. The height of each prism gives the local maximum water height at the fringe location. Three types of theoretical prism configurations (isosceles flat-topped prism, scalene flat-topped prism and rounded-topped prism models) have been studied for two flow systems: shooting flow around a wedge and around a cylinder. Equations relating the physical characteristics of the deviated fringes to the height of the theoretical prism and hence the local water height are presented. The variation in water height along a hydraulic jump for flow around a wedge obtained using the optical technique has been compared with heights obtained using a depth gauge. The results were in good agreement for the range of Froude numbers studied (Fr=1.9−3.6). The rounded-topped prism model led to the best agreement with the physical measurements, within 11% throughout the range of conditions studied. The uncertainty associated with the water height determination using the optical technique is ±10%.