The Flow of Swirling Water Down a Vertical and an Inclined Tube
Proceedings of the Royal Society A
P la te 16] W ater w ith a controllable am o u n t of swirl was a d m itte d to a long Perspex tu b e w hich could be held a t an y angle. A t tappings along th e tu b e , th e wall pressure an d th e a ir core diam eter were m easured, colour b ands were inserted a t various radii, a n d to ta l-h e a d trav erses across th e stream were m ade. F ro m these observations th e d istrib u tio n w as determ in ed of th e axial an d tan g en tial com ponents of velocity, w hich were a b o u t 10 to
... 15 ft./s. E x p erim en ts were m ade w hen th e o u tlet was p a rtly blocked, causing a ju m p to form , an d also w hen it was u nobstructed as in a 'v o rtex d ro p '. F o r b o th sta te s th e inviscid th e o ry of th e m o tio n is d eriv ed ; b u t agreem ent w ith th e experim ents is n o t close because, as in sw irling flow th ro u g h a nozzle, th e shearing action in th e stream w as intense. The core som etim es assum ed a helical shape of its own accord, an d alw ays to o k th is form a fte r th e stream h a d been forced ro u n d a bend. O bservations of these effects are com pared w ith th eoretical analysis. I n t r o d u c t i o n In a previous paper (Binnie 1964) on annular hydraulic jumps in a vertical tube, photographs were shown of the three possible forms. The jumps were undular, turbulent, or a mixture of the two which can be conveniently described as semiundular, all analogous to the well-known types which can be produced in rivers and channels; a closer analogy, however, is to a stream, not of uniform density but stratified. As the experiments were on a very small scale the description of them was principally qualitative, and the work has now been continued with a bigger tube so that it has been possible to attem pt more detailed measurements. The large reservoir, which in the previous experiments efficiently steadied the incoming flow at the cost of dissipating most of the supply of angular momentum, was replaced by a smaller one. This could be connected either to the normal labora tory supply at 40 ft. head or to a high-pressure pump. The internal diameter of the Perspex tube in which the jumps were formed was increased from 2 to 4f in., and the tube was attached to a frame that could be inclined at any angle to the vertical. Thus the range of the experiments was greatly widened. Details of the apparatus and the measuring instruments are given in § 2. For comparison with the experiments, theoretical expressions for the changes in Fronde number and radial depth at a fully turbulent jump are derived in § 3, and the con sequences of various assumptions concerning the downstream conditions are examined. A description of the experiments follows in § 4. The variation of wall pressure along the tube is shown for various water supplies and tube inclinations. Colour bands were introduced to indicate the direction of the streamlines, and numerical details of a typical turbulent jump have been worked out. t Present address: Snowy M ountains Hydro-electric A uthority, A ustralia.