An experimental study of the flow of water in pipes of rectangular section

Abstract

During the course of study, by the authors, of the flow of fluids in the small clearances which exist between the moving and fixed parts of certain machines, an accurate knowledge was desired of the range over which the equations of viscous flow could be applied. An exhaustive search revealed an absence of any record of experimental work which could be of direct assistance. An investigation was accordingly undertaken with the object of obtaining the desired information, and as the preliminary results were of an interesting and unexpected nature, the experiments were extended to cover the whole range of velocities and dimensions permitted by the apparatus. They have shown briefly that the lower critical velocity (as ordinarily understood) for flow between flat plates occurs at a value of the Reynolds number about one-half that found for pipes of circular cross section, if the linear dimension in that number is the distance between the plates and the diameter respectively. For velocities well below this limit there is evidence, however, of a distinct deviation from true viscous flow if initial disturbing factors are present, and the influence of such disturbing factors does not disappear entirely until a second well-defined limit is reached, which has a value of about one-tenth of the lower critical number. It would appear that below this limit eddies do not exist at any point in the pipe, and the flow is truly viscous. The suggestion is accordingly made that there may be three distinct types of flow: ( a ) one in which eddies cannot exist, corresponding to truly viscous flow; ( b ) one in which eddies may exist, due to an initial disturbance, but cannot be sustained in the pipe, the initial eddies therefore ultimately disappearing; and ( c ) one in which eddies once generated will be maintained without decrement throughout the pipe, corresponding to truly turbulent flow. The use of a channel of rectangular cross section for a study of the fundamental laws of the flow of fluids possesses advantages, in point of simplicity, which were recognised at once by Reynolds in his classical research into the cause of instability of flow. In the form in which this channel is used by the present writers, an additional and important advantage is obtained over the circular pipe by the fact that the controlling dimension may be varied over a wide range whilst retaining the same surfaces as boundaries. It is, in essentials, an adjustable pipe. The upper plate A (fig. 1) and the lower plate B are brass castings suitably drilled to provide inlet and outlet passages and pressure measuring points. The surfaces forming the pipe are hand scraped to a surface plate, and are separated at the ends by brass foil shims of suitable thickness, thus providing a passage between the inlet and outlet ports. The sides of this passage are closed by the plates C and D, very thin rubber insertion providing a watertight joint. All parts are sufficiently robust to reduce distortion under pressure to an amount found to be negligible.