Hydraulic Jump - Easy to setup, numerous options for research

Topic: Fluid Dynamics

The first section on the Experimental Research Ideas page is for Fluid studies. The reason for this is that there are many studies and situations one can dream up involving fluids that have not been studied in great detail, if at all. It is possible to look at past studies on fluid dynamics and think of different ways to 'tweak' the system that was studied and make it your own, original study. Perhaps my personal favorite is what is called the hydraulic jump.

The hydraulic jump has been studied for over a century, but because it involves turbulence, it is still not entirely understood. Turbulence, being a feature that involves random processes, is what allows fluid studies to have such a vast richness and variety, and each new discovery and observation is a contribution to the field. I cannot think of an easier experimental system for fluids to setup than the hydraulic jump. You literally see a jump every day of your life in sinks, bathtubs, or drinking fountains. When a stream of water lands on a hard surface, it flows outward in a smooth circular pattern, until suddenly the water lifts up, or jumps, to form a turbulent region. Don't get me wrong, while easy to create, a hydraulic jump is not easy mathematically - fluid dynamics is governed by the Navier-Stokes equations, which are presently unsolvable with exact solutions due to turbulence. Solving these equations numerically in computer simulations is the best we can do, and those theoretical studies have become very sophisticated. But a very rich set of experimental options is what we are after!

The different experimental options below, and some new ones that someone else may develop, all came from an activity I do with students. In about 15 minutes, a list of possible experiments can be developed for the jump. This process can be used for any everyday phenomenon, to break it down into possible parameters or quantities that might affect what you see, and give you possible experiments for that phenomenon. An example lesson and video are available to learn how to use this process (for hydraulic jump, in this case).

The novel research possibilities now become possible once you have a setup in your basement or kitchen, where you have a water source that can fall in a smooth stream or 'jet' onto a surface. The best way to collect measurements and other data is through video techniques. Be sure to have a grid and/or rulers in the video or photos in order to calibrate and scale for distance measurements. One can get radial and height measurements from video and digital photos, using software such as Tracker or LoggerPro, which many schools have; Tracker can be downloaded for free.

There are several student studies and papers serving as examples on the Experimental Research Ideas page, for certain types of hydraulic jump studies. Check those out for details on experimental setups and procedures. All of the following will be similar in their design, but differ in the physical situation that might affect the jump. We have not found any formal or detailed studies of these in the literature. Almost all of the suggestions below could be done in a combination of qualitative and quantitative studies. It is suggested that for quantitative studies, make plots of data and obtain fits for varying the variable quantity versus the radius of the jump, trying to develop an empirical formula for the radius that may be added into accepted mathematical models for the hydraulic jump.

• A basic study involves creating a stationary hydraulic jump on a flat surface, and find the relationships between the radius of the circle that forms and the flow rate, type of surface (materials, with different coefficients of friction), height from which the water stream falls, and even the viscosity of the fluid (try other liquids in addition to water). These studies have all been done over the years, but can be replicated if you just want to try the experimental setup and is also good for calibrations with past studies.
• Effect of a tilted surface on the jump structure; try a wide range of angles, is there a mathematical relationship one can find that fits the shape of the jump on inclines. See an example.
• Study of the interactions between multiple hydraulic jumps - have multiple streams/jets on the same surface at different distances between the jumps; can have each jet with the same or different flow rates. We have done this with two jumps, but try any number of jumps and see what patterns are created. See an example.
• Multiple jumps, but with different fluids - how are patterns affected when different fluids interact
• What does a jump look like and behave if the jet is a mix of two or more fluids? Could have two pipes with two different liquids flow together to make a single jet.
• The effect of having obstacles in the laminar portion of the flow on the surface, which allows for numerous studies just by varying the size, shape, and number of obstacles. Could also put obstacles in the region where the jump occurs and study what happens. For instance, obstacles just before, inside, and just outside the radii range of where the jump is forming. The obstacles could be small enough to be under the fluid surface or taller so it breaks through the surface.
• Effect of scratches in the surface on both the laminar and turbulent flows of the liquid. 
• Effect of the jet landing on a 3-D surface rather than a flat, 2-D surface. Are there still hydraulic jumps? What conditions must exist for a jump to form on a 3-D surface? Could try curved surfaces, funnel-shaped, pyramid shaped, and so on. 
• Effect of surface temperature on the jump.
• Polygonal jumps using viscous fluids (see a highly technical article).
• Jumps created on vertically oscillating surfaces; or jumps created on a 'see-saw' oscillating surface.
• Jumps on horizontally oscillating surfaces.
• Jumps created on rotating surfaces.
• If you have access to high-speed video, the time evolution of a hydraulic jump - film it from when the jet hits the surface and examine how the fluid flows outward and watch the formation of the jump.
• Does a jump form if there is a thin layer of stationary liquid sitting on the hard surface? What if the layer and jet are two different liquids?           
• Project a stream horizontally onto a vertical surface/wall, is there anything resembling a hydraulic jump? Investigate the properties of whatever pattern/structure forms.