In this blog post, we’ll explore the principle and process of a hydraulic jump—a phenomenon easily observed in rivers and sinks—as well as changes in the energy of fluids.
What Is a Hydraulic Jump?
During the rainy season, when heavy rains fall, news reports often show rivers swelling and overflowing their banks. If you observe the flow of the river closely at such times, you’ll notice that the water doesn’t flow in a single direction; instead, waves form as if the water were flowing upstream, creating undulations on the water’s surface. At first glance, it’s easy to assume this is an irregular phenomenon caused by obstacles on the riverbed, but it is actually a classic phenomenon that has long been studied in fluid mechanics. It can be explained theoretically and is covered as an important example in various fluid mechanics textbooks. Scientists refer to this phenomenon as a “hydraulic jump.”
A hydraulic jump observed in a river is a phenomenon in which rapidly flowing water suddenly slows down, causing the water level to rise sharply. These characteristics can be seen in the river photos featured in this article; the section where the water level suddenly rises and rough waves form is precisely where the hydraulic jump occurs.
A hydraulic jump is a phenomenon defined in hydraulics; it refers to the sudden increase in water level that occurs when a fast-flowing fluid enters a region of relatively slow-moving fluid. Simply put, it can be understood as the process by which the kinetic energy possessed by the fluid is converted into potential energy. However, the actual phenomenon is slightly more complex than this. A portion of the fluid’s initial kinetic energy is irreversibly dissipated during the formation of turbulence and converted into thermal energy. In other words, not all of the kinetic energy is converted into potential energy; a significant portion is consumed in the process of generating turbulence.
Here, turbulence refers to a flow in which different parts of the fluid move irregularly over time and space and mix with one another. This turbulence is particularly active in the sections where hydraulic jumps occur, causing rough waves, eddies, and spray to form. Therefore, sections of a river where strong waves suddenly form are not simply areas with fast-moving water, but rather regions where energy transformations within the fluid occur intensively.
Hydraulic jumps can be easily observed in our daily lives. The most representative example is the kitchen sink. When you turn on the faucet and let water flow onto the flat bottom of a sink, a thin, circular sheet of water initially spreads out at a very high speed. However, at a certain distance, the water level suddenly rises, forming a thick layer of water, and you can observe rough turbulence appearing on the outer side of this layer. This boundary is precisely where the hydraulic jump occurs.
If you increase the water pressure to make the water flow faster, you can easily observe that the location of the hydraulic jump shifts outward and the turbulent region expands. Conversely, if you reduce the flow rate, the hydraulic jump moves inward, and the scale of the turbulence decreases. Thus, the phenomenon observed in a sink is explained by the same physical principles as the hydraulic jumps that occur in rivers or dams.
A hydraulic jump is not merely an interesting natural phenomenon; it is a prime example of how the kinetic energy of a fluid changes and is dissipated. Understanding this principle facilitates not only the design of various hydraulic structures—such as rivers, dams, spillways, and gates—but also a clearer understanding of various fluid phenomena observed in nature.
Hydraulic jump cannot be fully explained by the law of conservation of mechanical energy alone; in actual engineering practice, it is analyzed using more sophisticated equations. In particular, engineers place great importance on the ratio of the water surface height before the hydraulic jump occurs to the height after it occurs. This value serves as a key indicator that quantitatively represents the scale of the hydraulic jump and the change in energy, and it is utilized in the design of various hydraulic structures.
In simplified fluid models based on various assumptions, this height ratio can be calculated; the most commonly used equation for this purpose is the Bélanger equation.
Bélanger Equation
The Bélanger equation is named after the French engineer Jean-Baptiste Charles Joseph Bélanger. This equation is a standard formula for calculating the relationship between water depth before and after a hydraulic jump, and it is still widely used today in the fields of hydraulics and river engineering.
In the equation, (v_0) represents the initial velocity of the fluid, and (g) represents the acceleration due to gravity. Since the acceleration due to gravity is nearly constant on Earth, the change in water surface height after a hydraulic jump is primarily determined by the fluid’s initial velocity and initial water depth.
What is interesting is that this equation explains fluid behavior based on the relationship between length and time rather than variables directly related to mass. Of course, in actual fluid flow, various factors such as pressure, viscosity, and turbulence also come into play; however, under ideal conditions, the Béranger equation can be used to predict the characteristics of a hydraulic jump with considerable accuracy.
The Béranger equation is not merely of theoretical significance. It serves as a crucial foundational reference in practical civil and hydraulic engineering fields—such as river design, spillway design, and the design of dam stilling basins—and is one of the essential calculation formulas for designing safe hydraulic structures.
Froude Number
The Froude number is a representative dimensionless number used to more simply determine whether hydraulic jump occurs. The Froude number is an indicator that expresses the initial velocity and initial water depth of a fluid as a single value, and it serves as a criterion for comparing the relative magnitudes of the fluid’s inertial forces and gravitational forces.
If the Froude number is less than 1 (Fr < 1), the fluid flows in a subcritical state, and hydraulic jump generally does not occur. Conversely, hydraulic jump occurs under decelerating conditions in supercritical flow, where the Froude number is greater than 1. In other words, as the Froude number increases, the kinetic energy of the fluid increases, and hydraulic jump becomes more pronounced.
The easiest example to observe this is a kitchen sink. When the faucet is turned on slightly, a thin water film forms, followed by relatively minor turbulence. However, when the water flow is increased further, the velocity of the water rises, causing the location where hydraulic jump occurs to shift outward, and the turbulent region becomes much thicker and more intense. These changes are typical phenomena that occur as the Froude number increases.
The Froude number is not used solely to calculate the height of the hydraulic jump. It serves as a fundamental design criterion in a wide range of fields, including the design of rivers and drainage channels, as well as the design of ships and offshore structures, port engineering, waterway design, flood analysis, and hydraulic model experiments. It is also used as one of the key dimensionless numbers for applying the law of similarity in flow analysis of moving objects such as automobiles and aircraft.
Ultimately, while the Béranger equation is the formula for calculating the results of hydraulic jump, the Froude number can be understood as a criterion for intuitively assessing the likelihood and magnitude of a hydraulic jump. These two concepts are closely interlinked and have established themselves as the most fundamental theories for understanding hydraulic jump in modern hydraulics and fluid mechanics.
Engineering Applications of Hydraulic Jump
Engineers designing dams use the Béranger equation and the Froude number to design spillways so that hydraulic jump occurs at the desired location. This is not merely to regulate water flow, but to prevent the immense kinetic energy of the fluid from being directly transferred to the structure, which could cause erosion or damage.
When a fluid flows at high speeds, continuous frictional forces act on the bottom and walls of a structure. In particular, when a hydraulic jump occurs, the flow transitions to turbulence, significantly increasing the vortices and irregular flow within the water; during this process, kinetic energy is effectively dissipated. Furthermore, as the Froude number increases, the energy retained by the fluid also increases, meaning the amount of energy dissipated through the hydraulic jump becomes greater as well.
To utilize this principle, structures such as spillways and stilling basins are installed at dams. Water flowing rapidly down the spillway intentionally induces a hydraulic jump in the stilling basin, dispersing its strong kinetic energy into turbulence and thermal energy. This reduces erosion in the downstream river and protects the dam body and surrounding structures.
Most hydraulic structures built today—including large dams, gates, weirs, canals, and drainage facilities—actively utilize this principle of hydraulic jump. By precisely designing the structure’s shape and slope, as well as the length and width of the spillway and the depth of the stilling basin, engineers ensure that the hydraulic jump occurs at the most efficient location. Therefore, the hydraulic jump is not merely a naturally occurring phenomenon but can be considered one of the key design elements that must be taken into account in modern hydraulic engineering.
Water Sports and Hydraulic Jump
On the other hand, there are those who welcome the hydraulic jump: kayakers, canoeists, and rafters who enjoy whitewater. As boats travel down rapids, they can utilize the unique water currents formed in sections where hydraulic jumps occur to perform various maneuvers.
In hydraulic jumps with a high Froude number, the fluid decelerates rapidly, forming a recirculating flow. This recirculating flow creates a pattern where water repeatedly circulates within a specific section; skilled athletes use this to remain stationary at a single point or perform various stunts with minimal effort. These techniques are frequently utilized in kayaking disciplines such as “hole surfing” or “playboating.”
Most world-famous whitewater sports destinations include sections where these hydraulic jumps occur naturally or have been artificially created. At locations where consistent hydraulic jumps are maintained, athletes can repeatedly practice their techniques, and they also provide a dynamic spectacle for tourists. Therefore, while hydraulic jumps are treated in civil engineering as structures designed to safely dissipate energy, in water sports, they become natural playgrounds that are actively utilized.
The Significance of Hydraulic Jumps
As such, a hydraulic jump is not merely a simple wave observed by chance in a river or sink. It is a representative fluid dynamics phenomenon in which the kinetic and potential energy of a fluid, the generation of turbulence, and energy dissipation all manifest in a complex interplay, and it holds great significance in modern hydraulic and civil engineering. Furthermore, as it is utilized in various fields—ranging from the safe design of dams and spillways to river management and water sports—it is regarded as one of the fluid phenomena where theory and practice are most closely intertwined.
When viewed through the lens of these principles, the ripples in a river or the stream of water in a sink—which we usually overlook—appear entirely different. Hidden within the small changes unfolding before our eyes are the complex laws of fluid dynamics and engineering design principles; the moment we understand them, even the ordinary flow of water around us becomes an intriguing scientific phenomenon.
