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The fastest river in the world. River velocity and circulation currents Average velocity of water flow in a river

The speed of the rivers. Discharge and runoff of rivers

flow speed runoff water

The role of flowing water on earth is enormous and has always attracted the attention of man, not without reason, since ancient times, many rivers have been personified; and in the eyes of modern science, rivers are the most active element of physical geography. Some of them are calm, have a slow current and regular rises in water, which are easy to foresee; others - quickly and swiftly carry stormy waters, suddenly raise their level and just as suddenly lower it.

But rivers are not only a geographical factor in themselves, but in themselves, they are at the same time tirelessly working to change the earth; the results of this geological work of flowing water, summing up over the centuries, are so great that the countries completely lose their original appearance: where once high mountains rose, at present we find only an undulating plain, and, on the other hand, high plateaus turned into mountainous or hilly areas.

Human life is in such close connection with the regime of flowing waters that the high interest shown by a person in relation to rivers is self-evident. The great rivers are the cheapest natural means of communication in many countries, and in the far north they are often the only means of communication, not only in summer but also in winter, when their icy surface offers the best way. Even in desert countries, as, for example, in the Sahara, dry riverbeds determine the direction of caravan routes. From time immemorial, Amu Darya (ancient Oxus), Syr Darya (ancient Jaxart) determined the direction of trade routes through Central Asia. The rapid colonization of certain countries, such as Canada, the middle part of the United States of America, and Siberia, becomes intelligible only if one takes into account the location of the rivers in these countries. The conveniences that rivers provide as means of communication draw people to their banks and are one of the factors in the emergence of cities, especially at the intersections of river routes. Rivers are even more important as mediators between the ocean and the interior of countries, not without reason, not far from their mouths, the greatest trading cities such as London, Rotterdam, Antwerp, Hamburg, Alexandria, Calcutta, Shanghai, Montreal, Quebec, New Orleans, Montevideo, Leningrad, etc. .

On the other hand, the floods of certain rivers, such as the Nile, Tigris and Euphrates, made it possible to develop civilizations at the very borders of the desert. The importance of rivers in the life of the country is so great that in all civilized states special organizations have arisen for the study of hydrography, and a systematic study of rivers and their regime has long been begun. In France, the establishment of the Service nydrometrique de la Seine preceded the establishment of meteorological stations, in Germany a number of valuable monographs were published on the study of all large rivers, from the Rhine to the Vistula, in the United States of America, a systematic study of rivers is carried out by the Geological Survey. The strong and devastating floods of the Danube, and especially its tributaries the Tissa, Maros and others in Hungary, led to the creation of a whole network of hydrological institutions with a central station in Budapest. Of the CIS rivers, the Dnieper, Volga and a number of other rivers were subjected to a more detailed survey in the 19th century; at the end of the 19th century, in European Russia, in addition, a special expedition worked to survey the sources of the most important rivers, under the general leadership of A.A. Tillo, which provided valuable material on the hydrology of the upper reaches of your main water arteries. The most characteristic feature of each river is its regime, i.e., the change during the year of its levels: flow, sediment, temperature, chemistry, etc. To find out the regime of a river, it is necessary to determine the relationship that exists between the amount of precipitation that has fallen in its basin, and a mass of water flowing down the river.

To determine this latter, it is enough to know the cross-sectional area of ​​\u200b\u200bthe river (the so-called living section) and the average speed of its flow in a given place, since the product of these two magnitudes gives us the required amount of water flowing by the river in a certain unit of time, for example, per second, per minute, etc. However, determining the flow of water in a river over a more or less significant period of time, and especially a whole year, is not an easy task, since both the flow rate and the living section of the river are constantly changing throughout the year.

The determination of the speed of the current is carried out either with the help of simple floats, such as bottles, or with the help of more accurate devices called turntables.

Observations show that the speed of the flow in the river usually decreases from the headwaters downstream. The reason for this is that during its movement, water experiences friction, both externally against the bottom, shores and against the air, and internally, due to the unequal speed and different direction of movement of water particles. In the end, the obstacles experienced by water during its movement are so great that they absorb all the acceleration acquired by water when falling from the sources to the mouth.

Due to friction in a given living section of the river, the highest speed (in the case of a regular river diameter) is in the middle, but not on the surface, but at some shallow depth, since on the surface the water experiences friction against the air. In the case of asymmetric living section, the highest speed will be over the deepest hollow of the river, closer to one of the banks. Connecting the points of the cross sections of the river, in which the current is the fastest, we get a winding line, which is called the core, or axis, of the river. A visual concept of the distribution of velocities in a given living section of the river can be obtained by connecting lines - isotachs - points that have the same speed. In the middle of the upper isotach runs the midstream of the river.

If there is no wind and the bottom roughness is normal, then on each individual vertical the highest speed will be from the surface at a distance of approximately 1/5 of the depth of the vertical.

The position of the point with the highest speed is determined by the ratio between the surface and bottom velocities (the ratio of surface and longitudinal friction). An increase in the bottom roughness will entail a decrease in the bottom velocity and a corresponding approach of the point with the highest velocity to the surface.

The water level in the river is not always the same. During the rise (rise) of water, its horizon in the middle of the channel rises slightly, and during the decline it drops in the middle and rises near the banks. This is due to the fact that the bottom of the channel near the banks creates resistance to the movement of water.


Scheme of a living current during a decrease and with a sharp increase in water

With a sharp decrease in water, all objects floating on the river (logs, debris, etc.) are drawn into its middle part, in a straight section of the channel and closer to the concave bank at its bend. This is especially well seen in the spring, when the flooded river enters the channel and individual ice floes and other floating objects move through the water, strictly outlining the ribbon-like contour of the rod.

During the rise of the water, various floating objects move along the banks, sliding off the water bulge formed in the middle of the stream. The splash is cut by the current, from which it becomes steep, the water has a dull yellow or dark color. With a decrease in water, the splash increases and becomes gentle.

The direction of the rod is especially pronounced where the current is strong, and its surface, wavy from the wind, is a light, clearly defined ribbon-like strip, interrupted in places.

Directions and velocities of currents can be determined by the navigator along the contours of the banks, based on the fact that the core passes close to the concave banks. If the coast is edged, then the current in the immediate vicinity of it is especially fast. The speed of the current is greater, the smaller the width of the channel and the greater its slope.

The direction and speed of the current can be determined by various coastal objects visible from the vessel: bushes, piles, stones, etc. At a high current speed, the water rises above these objects, forming a backwater.

The flooded bushes, under the pressure of the current, rhythmically sway, vibrate, and waves move away from rigid objects - pillars, piles, bridge supports. The greater the flow velocity, the sharper the angle of wave formation and the higher the wave. With a small current, a weak trace is visible below the object.

The direction and approximate speed of the current are determined by objects floating on the surface of the water, including those thrown into the water specially for this, and by the location of the angle of the rafts on which the buoys are installed. The stronger the current, the more the buoys and milestones tilt.

The headwind, increasing friction, reduces the surface speed and removes the highest speed from the surface. If the surface velocity is equal to the bottom one, the highest velocity will be in the middle of the vertical. In winter, under the ice, with a very rough bottom surface, the greatest speed moves closer to the bottom.

The wind blowing in the direction of the current will not slow down the surface layers of water, but will drive them, so the highest vertical speed will rise to the surface.

Thus, the flow velocity is determined by:

  • 1) the slope of the river surface,
  • 2) the shape of the channel,
  • 3) the roughness of the channel.

In this case, it must be borne in mind that the speed is determined by the slope of the water surface in the river, and not by the slope of the channel. If the surface of the water is horizontal (for example, in front of a dam), then there will be no current.

The Chezy formula, giving the dependence of the speed on the factors that determine it, makes it possible to foresee how the speed will change when these factors change.

Due to the unequal speeds of water movement in the living section, the surface of the river is not horizontal; as the river level rises, more water flows to the middle than to the edges, and the surface takes on a convex shape, which is very clearly seen, for example, in our rivers before the ice breaks up: due to the increase in water, ice also takes a convex shape towards the middle, and surface melt waters are collected near the shores, forming here long puddles, while the surface of the ice in the middle remains dry. When the waters subside, the largest amount of water flows down the middle of the river, and the surface of the river takes on a concave shape. The resulting level difference in the Mississippi reaches 2 m.

In addition, the transverse profile of the river is distorted by the centrifugal force, the Coriolis force resulting from the rotation of the earth, and the surge winds blowing across the river. There are two types of fluid motion - laminar and turbulent.

If the speed at each point is depicted as a vector (an arrow giving the direction of the speed and its magnitude), then during laminar motion the speed vector at each given point will be constant and will not change. Such fluid motion is observed in narrow tubes at low velocities. In nature, the movement of groundwater through small pores approaches laminar. A special case of laminar motion will be parallel jet.

Turbulent motion is characterized by inconsistency, variability of the velocity vector at each given point of the live section or vertical. This variability is called pulsation. Thus, during turbulent motion, each individual particle of water, arriving at a given point, will pass it in different directions and with different linear speeds. Turbulent motion is widespread in nature. All sufficiently fast-flowing surface waters are turbulent. It is safe to say that rivers have only turbulent flow. A special case of turbulent motion is vortex (whirlpools, funnels, etc.).

The velocity vector of turbulent motion can be decomposed into components - horizontal, vertical and lateral. The horizontal component characterizes drift downstream, and the vertical component characterizes the movement of water particles up or down.

The significance of the turbulence of the river flow is extremely high. It determines the mixing of river water and the transport of material in suspension.

The amount (volume) of water flowing through the living area per unit time is called the flow of the river. The flow over a long period of time is called runoff. Usually there are annual, monthly, daily runoff.

Knowing the mass of water flowing by the river at different times of the year, we can get an idea of ​​its regime. For clarity, the change in water flow can be expressed graphically, denoting the amount of water flowing at a given time with rectangles proportional to the corresponding masses of water. Since the determination of the discharge is associated with great difficulties and has been made for a small number of rivers, they are often limited only to observations on the water gauge over fluctuations in the level of the river, and on the basis of these fluctuations they also judge the change in discharge, obtaining empirical formulas for the dependence of the discharge on the height of the level. These formulas lose their meaning if the channel is unstable (washed out or covered).

Precipitates deposited on the surface are known to run off, dissolve, and percolate. The leaked water will sooner or later either evaporate or join the drain, therefore, on average, over a long period of time, it can be considered that the precipitated water partly evaporates and partly drains. If the runoff coefficient is 30%, then this means that out of the total amount of precipitation, 30% is glass, and the remaining 70% has evaporated.

The value of the runoff coefficient is determined by the general geographical situation - climate, relief, vegetation. So, for the rivers of northern Europe - the Neva, Northern Dvina, Pechora, etc. - the runoff coefficient is more than 60%, for the Don it is about 15%, for the Nile - about 4%, for the Amazon - about 30%. Huge evaporation in the Nile basin and weak in the north of Europe and gives such a sharp contrast. In different years, for the same river, the runoff coefficient varies depending on the amount of precipitation. In wet years, the runoff coefficient is greater, in dry years it is less.

In drainless areas, the runoff coefficient is zero.

Among the reasons that determine the runoff coefficient, the climate of the area must be put in the first place. Temperature influences the form of precipitation and the course of evaporation. High temperatures and low humidity reduce surface runoff and shut down shallow springs. During winter dormancy, the evaporation of vegetation stops, the frozen soil prevents the penetration of water into the depths. In areas with long cold winters, the snow that has fallen for the winter remains until spring. In the spring, the runoff coefficient is greatly increased by melt water.

The relief also affects the value of the runoff coefficient: a significant slope facilitates runoff even on permeable rocks. Mountain streams after rain carry an enormous amount of water, and in the absence of rain they almost dry up, not due to lack of precipitation, but due to the fact that their waters drain too quickly. Permeable rocks cause a more uniform runoff, impermeable rocks - the flow regime.

In mountainous areas, the forest has a beneficial effect on the regime of rivers, slowing down the flow of water and thereby protecting mountain slopes from erosion. In general, the forest has a regulating effect on river flow, reducing the size of the flood and maintaining moisture reserves by the beginning of summer. Swamps, contrary to popular belief, are unfavorable for feeding rivers. Peat, like a sponge, absorbs a lot of water in wet times, and evaporates a lot in hot weather. According to Oppokov's research, the drainage of swamps not only does not entail the shallowing of rivers, but contributes to their more proper nutrition.

In addition to the runoff coefficient, the runoff modulus is also used to characterize the runoff.

The runoff module is the amount of water, expressed in liters, flowing down on average in one second from 1 sq. km of basin area. Engineer Kocherin built a contour map of the runoff module for the European Union Territory. Knowing the average basin runoff modulus, one can calculate the annual runoff value by multiplying the runoff modulus by the number of seconds in a year and by the basin area. It is also clear that the runoff modulus is closely related to the amount of precipitation, evaporation, topography, vegetation, and surface character.

    The speed of the current depends on the width of the channel and the height difference. It is measured with a hydrometer. 5 measurements are made at a certain depth in different areas. The current speed in the Amazon, which is considered the fastest river, is 4.5-5 m / s. or about 15 km/h.

    A river from South America - the Amazon is considered the river with the maximum flow rate.

    According to research results, this river is the longest in the world. In addition, you can only cross the river by ferry, bridges over this river have not been built because of its decent width.

    The average speed is about 15 km/h. But during high tides from the ocean, the Amazon moves even faster.

    As for the maximum speed of a particular river, I could not find information, so I will not say. The speed of the current depends on: 1 the relief and the underlying surface. Plain rivers or rivers in flat parts are much slower because there is no slope and the water does not pick up a certain speed. On the plains, water flows more slowly and because of the restraining factors of the underlying surface, the earth, which is looser than rocks. 2. From wind speed. The wind is a definite push for the water, forming a wave. 3. The dynamics of river movement also depends on the amount of sediment, i.e. the natural or man-made material that water carries. A large amount of sediment slows down the movement of water. There are other factors, but these are the most prominent.

    The Amazon is considered the fastest river. Measure the speed of the current in meters per second. But, of course, the speed of the river changes along its entire length: at the source it is less than at the mouth, and it is maximum in the middle reaches of the river, where the speed also increases due to the power of the water flow. The speed of the current depends on the power of the water flow and on the slope of the terrain along which the river flows. The average velocity is calculated from several measurements, usually at five different points in the channel. In the Amazon, this is 4.5-5 m / s or 10-15 km / h. The Amazon is also the longest, full-flowing and deepest river in the world.

    As far as I remember from school geography, the Amazon is the fastest river in the world. The speed depends on the slopes where the river flows. There is an upper, middle and lower course. In the upper reaches, the speed is the highest.

    In general, any river the speed of the current is not constant along the entire length of the river- it varies both in depth and width. To determine the average speed rivers do at least 5 measurements in different places - at the source, middle and mouth of the river.

    Required items:

    1) hydrometric turntable

    2) auxiliary equipment - gauging rod, rope, swivel, gauging weights and winches.

    3) stopwatch.

    What affects the speed of a river

    1) The slope of the channel, as well as its width - the speed is directly dependent on the slope of the channel.

    2) Terrain - mountain rivers have a faster flow.

    3) Irregularities at the bottom of the river - the speed in the stream in front of the obstacle in this case decreases sharply towards the bottom.

    4) Wind - if the direction of the wind is against the current, then the speed of the river decreases.

    5) The presence of aquatic vegetation.

    The fastest river

    She is a South American river Amazon- she has an average speed 4.5-5 meters per second or 15 kilometers per hour.

    Amazon also owns a number of records:

For determining water flow in the river still to be determined average speed of the river. This can be done in various ways:

  1. surface floats;
  2. by maximum speed;
  3. using hydrometric poles or milestones;
  4. using deep floats;
  5. hydrometric turntables.

Determining the speed of the river flow by surface floats.

Choosing a straight section of the river,

  • we install 8 rails (milestones) in pairs on both banks, one behind the other;
  • each pair of rails should be placed perpendicular to the direction of the river flow;
  • the distance between the rails that make up a pair must be the same for all pairs (for example, 5 m each).

Thus, we establish four alignments: I-launching, II - upper, III - main, IV - downstream of the river.

These sites are at the same distance from each other, the value of which depends on the size of the river, for example, at a distance of 15 m from each other.

Before throwing the floats, you need to record the start time of work, and after the end - the end time of work; then note the work environment:

  1. the state of the river at the hydrometric section (clean, in some places covered with vegetation);
  2. weather conditions (clear, overcast, fog, rain);
  3. wind characteristics (calm, weak, medium, strong; downstream, against the current; from the left or right bank);
  4. characteristics of the flow surface (calm, rippled, rough).

The wind has a particularly great influence on the speed of the river flow: it increases (tail wind) or reduces (head wind) the flow speed, therefore, for greater accuracy in determining the flow speed, corrections are made. For the introduction of amendments there are special tables.

Further, placing the observers on the alignments, you can start throwing floats. Floats are usually used in the form of circles sawn off from dry logs with a diameter of 10-25 cm and a thickness of 5-6 cm. To make the float better visible on the river, it is painted with white paint, and sometimes bright red. If the river is small, then you can limit yourself to three to five floats.

At the launch site, the floats are thrown sequentially: first closer to the right bank, then to the middle of the river, then closer to the left bank.

A signal is given at the top. When the float is in the target, the observer standing at the main target marks the time, that is, starts the stopwatch or simply notes the time on the clock with a second hand. The observer standing at the lower alignment, when the float passes through the alignment, gives a signal to the observer at the main alignment, and he stops the stopwatch or notes the time on the clock. To determine the speed of movement of the floats, it is more convenient to conduct observations according to the following table.

If the distance between the alignments is 15 m, then the distance between the upper and lower alignments will be 30 m. etc.) and get the data that is recorded in the table below.

float number

Float path (m)

Float stroke duration (sec)

Current speed (m/s)

Average surface current velocity (m/s)

We divide the path of the float by the time of its movement and find out the speed of the float, and to determine the average speed of the current, we add the speeds of all floats and divide by their number.

Determining the average speed for small rivers from the maximum surface speed.

We multiply the highest speed Vmax by the correction factor K, which depends on the degree of roughness of the channel. The result is the average speed of the river. For mountain rivers with a boulder bottom, K = 0.55, for rivers with a gravelly bottom, K = 0.65, for rivers with uneven sandy and clay beds, K = 0.85. For example, if K = 0.75, then the average speed in our example

Vav = 0.75-0.65 - 0.49 m/sec.

Determination of the average flow rate using hydrometric poles or milestones.

To do this, take a gauging pole with a length less than the minimum depth on a given section of the river, otherwise the pole will get stuck in shallow water. A stone of such a size is tied to the pole that the hydrometric pole protrudes slightly above the water, and its speed is determined at different points in the river in the same way as is done with surface floats; find out the average speed. In this case, the average speed will not be surface, but along the living section, but for greater accuracy, a correction should be introduced according to the formula:

where H is the average depth of the river from the water surface to the bottom, h is the depth of the gauging pole, v is a certain speed.

Determination of average speed using deep floats.

To determine the speed in this way, you need to take two bottles. The bottles are tied to each other with a string, the length of which will depend on the depth of the river being explored. One bottle (lower) is filled with water and corked, sand is poured into the second bottle (upper) in such an amount that only part of its neck is above the water, and also corked.

Observing the top bottle, determine the average speed of both bottles. Using two bottles, you can also determine the speed at a certain depth equal to the depth of the bottom bottle. For example, we want to determine the speed at a certain depth of the river on a given segment. Then, tying the bottom bottle to a depth of 0.2 h (where h is the depth of the river), we first determine the average speed of the two bottles - the top and bottom, i.e. vcp, and with the help of surface floats we determine the average surface velocity Vav.

and find the desired speed by the formula:

V 0.2 h = 2 Vav - Vav.

This method can also determine the speed at depths: 0.4 h; 0.6h; 0.8h; thus, we can find out the average speed from the living section. To do this, add all five speeds, and divide by 5:

Observations show that flow velocities are unevenly distributed over the cross section of rivers. They reach their maximum value either on the freest surface, or at an insignificant depth from it. As you get closer to the bottom, the speed decreases. The picture of the distribution of speeds can be depicted on the graph. To do this, the depth of each point is plotted vertically (top to bottom), and the flow velocity horizontally (left to right). Connecting the ends of the horizontal lines representing the flow rates, we get a curve called speed hodograph.

Knowing the average flow velocity and the open area, we can determine water flow in the river according to the formula:

For example, above we determined that F = 7.08 m2, and the average speed Vav = 0.27 m/s; hence Q = 7.08-0.27 = 1.91 m3/sec. Rounded can be considered Q==2 m3/sec.

Now we determine the water flow in our second example by the formula: Q = F- Vav, where F = 7.4 m2, and Vav = 0.4 m/s; Q - 7.4 * 0.4 \u003d 2.96 m3 / s, Rounded can be considered Q = 3 m3 / s.

Determination of fluctuations in the water level in the river.

If possible, then with the help of a water gauge, follow the fluctuations in the water level in the river within a few days. Usually the water level is measured once a day, at 8 o'clock in the morning; if this is difficult, then observations can be made once every 10 days, and daily observations can be made only during floods or floods. The difference between high water level (h max) and low water level (h min) is called oscillation amplitude(A) water level.

The magnitude of the amplitude is of great importance in the design of various hydraulic structures.

To monitor the fluctuation of the water level in the river, one can take the conditional water level at the depth of the pile, which never leaves the water during the year. From this conditional level, called the zero of the graph, a graph of the fluctuation of water in the river is drawn.

In general, the zero of the graph is taken as the water horizon deeper than the minimum water level, which can be found at the nearest gauging station. When plotting a graph, the time of determining the depth is plotted on the abscissa axis, and elevations above the zero of the graph or the water level mark for each day are plotted on the ordinate axis.

The Amazon is moving at a speed of 15 km/h

The Amazon River is considered the fastest river in the world, already having several titles of the “most-most”. Among them, such titles as the most full-flowing (7,180,000 km 2), the deepest (its depth in some places reaches 135 meters), the longest (7,100 km) and the widest (in some places the Amazon delta has a width of 200 km) . In the lower reaches of the Amazon, the average water flow is approximately 200-220 thousand cubic meters, which corresponds to a river flow speed of 4.5-5 m/s or 15 km/h! In the rainy season, this figure increases to 300 thousand m 3.

The course of each river consists of the upper, middle and lower reaches. At the same time, the upper course is characterized by large slopes, which contributes to its greater erosive activity. The lower course is distinguished by the largest water mass and lower speed.

How is the flow rate measured?

The units used to measure the speed of a river are meters per second. At the same time, one should not forget that the speed of the water flow is not the same in different parts of the river. It gradually increases, originating from the bottom and walls of the channel and gaining the greatest power in the middle part of the stream. The average flow velocity is calculated on the basis of measurements made in several sections of the channel. Moreover, at least five spot measurements are carried out on each section of the river.

To measure the speed of the water current, a special measuring device is used - a hydrometric turntable, which descends to a certain depth strictly perpendicular to the surface of the water and after twenty seconds you can take the readings of the device. Given the mean velocity of the river and its approximate cross-sectional area, the water discharge of the river is calculated.

Reverse flow of the Amazon

In addition, the Amazon River is the owner of a reverse current that occurs during ocean tides. Water flows with great speed - 25 km / h or 7 m / s, are driven back to the mainland. Waves at the same time reach 4-5 meters in height. The farther a wave passes on land, the less its destructive effect becomes. The tides stop at a distance of up to 1,400 kilometers upstream of the Amazon. Such a natural phenomenon was called "pororoka" - thundering water.

The average flow velocities vary along the length of the river due to the variability of the size of the cross section of the channel. In a particular transverse alignment, the average speed is found by averaging local velocities measured at individual points in the flow along the depth and width of the river. In turn, local velocities at different points in the flow differ significantly from each other. At the surface, they are usually larger than at the bottom, and near the banks, on the contrary, they are less than in the middle part of the river.

This distribution is strongly influenced by the shape of the cross section of the channel and the conditions of water movement in the area.

The presence of vegetation or other additional roughness at the bottom of the river leads to a decrease in the near-bottom water flow rates. The formation of ice cover on the free surface in winter creates additional resistance to the movement of water. As a result, the surface flow velocities decrease, and the maximum velocities move into the bulk of the flow. This leads to the fact that the average speeds in the cross section of the river also decrease in winter compared to the summer period, all other things being equal.

To analyze the distribution of local flow velocities over a living section, in practice they are measured at individual points along the flow depth on a whole series high-speed verticals, planned along the width of the river. On fig. 4.4 shows the profile of the cross-section of the riverbed with the measured flow velocities on the verticals. In this example, the current velocities were measured in 5 points along the flow depth. The profile of the river shows isotachy - lines of equal velocities in the cross section of the channel.

At the top of the building is shown diagram the distribution of average current velocities on the verticals along the width of the river, and the dotted line is the value of the average flow velocity over the living section.

According to the measurement of water flow rates at individual points along the depth of the flow, it is possible to build diagram their vertical distribution. An example of such a construction is shown in Fig. 4.5. On the vertical axis on this graph, the distances from the free water surface to the speed measurement points are plotted on a scale, and the values ​​of these speeds are plotted along the horizontal axis. The average vertical speed is usually at a distance 0.4h counting from the bottom of the river.

In each specific case, the distribution of flow velocities along the vertical and along the width of the channel depends on the conditions of water movement in the area. Usually, the maximum surface flow velocities and the highest average flow velocities on the verticals are observed in the region of maximum depths in the free section of the channel. On the riffles, the diagram of average current velocities is aligned along the width of the river compared to the reach hollows. The greatest uneven distribution of velocities along the width of the river is observed in the sections of the channel turn. In this case, the maximum flow velocities are concentrated at the concave - the pressure side of the river. On fig. 4.6 shows the distribution diagrams of the average vertical flow velocities in the erratic section of the river.

Rice. 4.6. Distribution of average current velocities

on the rift of the river

An analysis of the distribution of flow velocities along the width of the river shows that on the core of the flow, in the deepest part of the channel, the actual flow velocities of water are always greater than the average over the living section.

Therefore, when performing technical and economic calculations, the concept is introduced operational flow rate, the value of which can be found from the following relationship:

, (4.8)

where: Vav - average flow velocity along the free section in the considered section of the river, m/s;

DV is the difference between the current velocity on the axis of the ship's course and the average velocity along the living section in a given river section, m/s.

The value of the average flow velocity can be determined by the Chezy formula or on the basis of field measurements. The flow rates in the river are measured by special instruments - hydrometric turntables(Fig. 4.7) or by starting the floats. Determine the value of a quantity DV direct measurements on a long section of the river is very difficult.

Rice. 4.7. Hydrometric turntable:

1 - blades; 2 - body; 3 - tail section;

4 - rod; 5 - electrical terminals

In practice, the operational speed for a particular section of the river is determined by measuring the speed of the vessel relative to the shore when following the flow Vin and against the current Vcc according to the formula

. (4.9)

For approximate calculations, it is often taken

Knowing the operational speed of the current, you can find the speed of the ship relative to the shore:

when moving downstream

, (4.11)

moving up against the current

, (4.12)

where: Vs - vessel speed in calm water (in the absence of current), m/s.

The obtained values ​​of ship speeds are used in practice when planning the time of delivery of goods and compiling dispatch schedules.

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During the construction of many engineering structures on rivers, it is necessary to know the amount of water flowing in a particular place per second, or, as they say, the flow of water. This is necessary to determine the length of bridges, dams, as well as for irrigation and water supply.

Water flow is usually measured in cubic meters per second. The discharge of water in high water is very different from the discharge in low water, that is, at low summer levels. Table 7 shows the costs for some rivers as an example.

If we mentally cut the river across the flow, we get the so-called "living section" of the river. The distribution of the flow velocity over the living section of the river is very uneven. The speed of the current is affected by the depth of the channel, and its shape, and the obstacles that the river encounters in its path, for example, a bridge support, an island, etc.

Usually, the speed is lower near the banks, and in the middle, in the deeper part of the river, the speed is much higher than in the shallow one. In the upper part of the stream, the speeds are greater, and the closer to the bottom, the less. On a flat section of the river, the highest speed is usually somewhat below the surface of the water, but sometimes the highest speed is also observed on the surface.

If the current encounters an obstacle, for example, a bridge support, an island, then the highest speeds can move closer to the bottom of the river. On oxbow lakes during floods, velocities near the bottom drop to zero.

Figure 14 shows the distribution of current velocities along the living section of the Volga near Saratov during the flood. The speed on the surface in the left arm is 1.3 per second, and in the right arm 1.7 per second. Over the island, which is covered with water during the flood, the speed drops to 0.5 per second. At the bottom of the river, the velocities drop to 0.4. In summer, the highest speed in this section in the main channel was no more than 0.4 per second.

Along the river, velocities can also vary greatly depending on the shape of the living section. For example, fourteen kilometers below Saratov, near Uvek, where the channel has no islands and is constrained by dams, during the flood the surface speed reached 3 per second, while at Saratov the speed was up to 1.8 per second.

In deep places on the river, which are called stretches, the free section is larger. In shallow places or rifts, the free section is much smaller. Since in a short section along the length of the river the water flow rates are equal, and the sections on the stretch are larger than on the rift, the flow rates will be different: in a deep place the water flows quietly, and on the rift it is much faster.

The speed of the current also depends on the slope of the stream, the roughness of the bottom and the depth. The greater the slope, the smoother the bed and the more correct its shape, the higher the speed of the current. Approximate speeds on rivers are shown in Table 8.

The table shows "average speed". This speed is determined by dividing the flow of water by the area of ​​the living section of the river. The highest surface speed is usually one and a half times more, and the bottom one is one and a half times less than the average speed.

The science of hydrometry is engaged in measuring the speed and flow of water in rivers.

The speed of water flow can be measured in a very simple way.

To do this, you need to measure a certain distance along the shore, at least in steps, set marks and throw a float or just a sliver into the water slightly above the top mark. The time for the float to pass from one mark to another is measured by a watch with a second hand. By dividing the distance between the marks by the time the float floated from one mark to the next, we get the surface flow velocity at that location.

On surveys, the passage of the floats is detected with a special goniometric tool.

Velocity can be measured most accurately using hydrometric turntables (Fig. 15). These turntables on a metal rod (at depths up to 4) or on a cable (at any depth) are lowered from specially equipped vessels into the water at different depths. As soon as the spinner makes a certain number of revolutions, the electrical wires in it are closed, current flows through the spinner, and a short bell is obtained from above. The time interval between individual calls corresponds to a certain flow velocity. Lowering the turntable lower and lower, one can measure the speeds throughout the depth of the river on a given vertical.

The flow of water in the river is calculated as follows. On each of 10–20 verticals located across the current at the same distance from each other, the average flow velocity is determined, which is then multiplied by the area of ​​the river's living section between the verticals. The individual private expenditures obtained in this way between the verticals are added up. The sum gives the total flow of the river, expressed in cubic meters per second.

In conclusion, we give some information about the ford crossing of the rivers.

Wading can be done, depending on the speed, at different depths. As a rule, at a speed of 1.5 you can wade at a depth of 1, on horseback - at a depth of 1.2, by car - at a depth of 0.5. At a speed of 2, you can wade at a depth of 0.6, cross the river on horseback - at a depth of 1, by car - at a depth of 0.3 If the water is still, the greatest depth for fording is determined only by the height of a person and the design of the car.

There are several ways to measure the speed of a river. You can do this when solving mathematical problems, when there is some data, or you can do it by applying practical actions.

river speed

The speed of the current depends directly on the slope of the channel. The channel slope is the ratio of the height difference of two sections, points, to the length of the section. The greater the slope, the faster the flow of the river.

What is the speed of the current of the river, you can find out by going on a boat along the river upstream and then downstream. The speed of the boat downstream is V1, the speed of the boat upstream is V2. To calculate the speed of the river you need (V1 - V2): 2.

To measure the speed of water flow, a special lag device is used, a spinner, consisting of a blade, a body, a tail section, and a rotor.

There is another simple way to find the speed of a river.

Measure upstream 10 meters, you can steps. Your height will be more accurate. Then make a mark on the shore with a stone or a branch, throw a chip into the river above the mark. After the chip is level with the mark on the shore, you need to start counting the seconds. Then divide the measured distance of 10 meters by the number of seconds for this distance. For example, a piece of wood swam 10 meters in 8.5 seconds. The speed of the river will be 1.18 meters per second.

Elements of the water regime and methods for observing them

(according to L.K. Davydov)

Under the influence of a number of reasons, which will be discussed below, the flow of water in rivers, the position of the level surface, its slopes and flow rates change. The cumulative change in water discharges, levels, slopes and flow rates over time is called the water regime, and the change in the values ​​of discharges, levels, slopes and velocities separately is called the elements of the water regime.

Water consumption (Q) is the amount of water that flows through a given living section of the river per unit time. The flow rate is expressed in m3/s. Water level (H) - the height of the water surface (in centimeters), measured from some constant comparison plane.

Level Observations and Processing Methods

Observations of level fluctuations are carried out at water measuring posts (Fig. 73) and consist in measuring the height of the water surface above a certain constant plane, taken as the initial, or zero. Such a plane is usually taken as a plane passing through a mark slightly below the lowest water level. The absolute or relative mark of this plane is called the zero of the graph, in excess of which all levels are given.


Rice. 73. Pile water metering post (a) and reading the water level on a portable rail (b).

Measurements are made using a water gauge with an accuracy of 1 cm. Reiki are of two types - permanent and portable. Permanent slats are attached to the abutments of bridges or to a pile driven into the bottom of the channel near the shore. With gentle shores and large amplitudes of level fluctuations, observations are carried out using a portable rail. To do this, a number of piles located in the alignment are driven into the riverbed and on the floodplain.

The marks of the pile heads are connected by leveling with the benchmark of the water measuring station installed on the shore, the absolute or relative mark of which is known. A portable rail mounted on the pile head measures the water level. Knowing the mark of the head of each pile, it is possible to express all measured levels in excesses above the zero surface, or zero of the graph. Observations at water measuring posts are usually carried out 2 times a day - at 8 and 20 hours. During the period when the levels change rapidly, additional observations are made every 1, 2, 3 or 6 hours during the day. For continuous recording of levels during the day, level recorders are used, the description of which can be found in the hydrometry textbook (V. D. Bykov and A. V. Vasiliev). There you can also get acquainted with the automatic regime registering (water level and temperature) hydrological post. The transition to an automated observing system accelerates the acquisition of hydrological information and increases the efficiency of its use.

From all measurements, the average levels for each day are calculated and tables of daily average levels for the year are compiled. In these tables, in addition, the average levels for each month and for the year are placed, and the highest and lowest levels for each month and year are selected.

The average, maximum and minimum levels are called characteristic levels. Level observation data are published in the USSR in special publications—hydrological yearbooks. In the pre-revolutionary period, these data were published in the "Information on the water levels on the inland waterways of Russia according to observations at water-measuring posts."

Based on the data of daily observations of levels, graphs of their fluctuations are constructed, giving a visual representation of the level regime for a given year.

Methods for measuring river flow rates

River flow rates are usually measured either with floats or hydrometers. In some cases, the value of the average speed for the entire open section is calculated using the Chezy formula. The simplest and most commonly used floats are made of wood. Floats are thrown into the water on small rivers from the shore, on large rivers - from a boat. The stopwatch determines the time t of the passage of the float between two adjacent gates, the distance l between which is known. The surface current velocity is equal to the velocity of the float

More precisely, the flow velocities are measured using a hydrometric meter. It allows you to determine the average flow velocity at any point in the flow. Turntables are of various types. In the USSR, modernized hydrometric turntables Zhestovsky and Burtsev GR-21M, GR-55, GR-11 are currently recommended for use.

When measuring speeds, a turntable on a rod or cable is lowered into the water to various depths so that its blades are directed against the current. The blades begin to rotate, and the faster, the greater the flow velocity. After a certain number of revolutions of the axis of the turntable (usually after 20), a light or sound signal is given using a special device. The number of revolutions per second is determined from the time interval between two signals.

Turntables are calibrated in special laboratories or in factories where they are manufactured, i.e., a relationship is established between the number of revolutions of the turntable blade per second (n rev / s) and the flow velocity (v m / s). From this dependence, knowing n, we can determine v. Turntable measurements are made on several verticals, at several points on each of them.

Methods for determining water flow

The flow rate of water in a given living section can be determined by the formula

Where v is the average speed for the entire open area; w is the area of ​​this section. The latter is determined as a result of measurements of the depths of the river channel along the transverse alignment.

According to the above formula, the flow rate is calculated only if the speed is determined by the Chezy formula. When measuring speeds with floats or a turntable on separate verticals, the flow rate is determined differently. Let the average speeds for each vertical be known as a result of measurements. Then the scheme for calculating the water flow is as follows. Water flow can be represented as the volume of a water body - a flow model (Fig. 76 a), limited by a free section plane, a horizontal water surface and a curved surface v = f (H, B), showing the change in velocity with depth and width of the flow. This volume, and hence the flow rate, is expressed by the formula

Since the law of change v = f (H, V) is mathematically unknown, the flow rate is calculated approximately.


Rice. 76 Scheme for calculating water consumption. a — flow model, b — partial flow.

The flow model can be divided by vertical planes perpendicular to the open area into elementary volumes (Fig. 76 b). The total flow rate is calculated as the sum of the partial flow rates AQ, each of which passes through a part of the free area wi enclosed between two high-speed verticals or between the edge and the vertical closest to it.

Thus, the total flow Q is equal to

where K is a variable parameter depending on the nature of the coast and changing from 0.7 to 0.9. In the presence of dead space K = 0.5.

The average speed for the entire open area with a known water flow rate Q is calculated by the formula vcr = Q / w.

Other methods are also used to measure water flow, for example, the ion flood method is used on mountain rivers.

Detailed information on the determination and calculation of water flow rates is given in the hydrometry course. Between water discharges and levels there is a certain relationship Q - f (H), known in hydrology as the curve of water discharges. A similar empirical curve is shown in fig. 77 a.

It is based on the measured water flow in the river during the ice-free period. The points corresponding to winter water discharges lie to the left of the summer curve, since the discharges measured during freeze-up Qwinter (at the same level height) are less than summer QL. The decrease in flow rates is a consequence of an increase in the roughness of the channel during ice formations and a decrease in the open area. The ratio between Qzim and Ql, expressed by the conversion factor

It does not remain constant and changes in time with changes in the intensity of ice formations, ice thickness and the roughness of its lower surface. The course of changes Kzim=f(T) from the beginning of freezing to opening is shown in fig. 77 b.

The flow curve allows you to determine the daily flow of river water from known levels observed at water gauges. For an ice-free period, the use of the Q = f(H) curve does not cause any difficulties. Daily costs during freeze-up or other ice formations can be determined using the same curve Q = f(H) and the chronological graph Kwm = f/(T), from which the Kwm values ​​are taken on the desired date:

QZIM = KZIM QL

There are other ways to determine winter costs, for example, according to the "winter" cost curve, if it can be built.

The unambiguity of the water discharge curve in some cases is also violated during the ice-free period. This is most often observed in an unstable channel (alluvium, erosion), as well as in the event of a variable backwater caused by a mismatch in the course of the levels of a given river and its tributary, the operation of hydraulic structures, overgrowing of the channel with aquatic vegetation and other phenomena. In each of these cases, one or another method of determining the daily water consumption is chosen, which is presented in the course of hydrometry.

According to the daily water consumption, you can calculate the average consumption for a decade, month, year. The average, highest and lowest costs for a given year or for a number of years are called characteristic costs. Based on the daily flow data, a calendar (chronological) graph of fluctuations in water flow is built, called a hydrograph (Fig. 78).


Rice. 78. Hydrograph.

River Flow Mechanism

(according to L.K. Davydov)

Movement is laminar and turbulent

In nature, there are two modes of fluid motion, including water: laminar and turbulent. Laminar motion - parallel jet. With a constant flow of water, the velocities at each point in the flow do not change in time either in magnitude or in direction. In open streams, the velocity from the bottom, where it is equal to zero, gradually increases to its maximum value at the surface. The movement depends on the viscosity of the fluid, and the resistance to movement is proportional to the speed to the first power. Mixing in the flow has the character of molecular diffusion. The laminar regime is typical for underground flows flowing in fine-grained soils.

In river flows, the movement is turbulent. A characteristic feature of the turbulent regime is the pulsation of the velocity, i.e., its change in time at each point in magnitude and direction. These fluctuations in speed at each point occur around stable average values, which hydrologists usually operate with. The highest velocities are observed on the flow surface. In the direction towards the bottom, they decrease relatively slowly and in the immediate vicinity of the bottom they are still quite large. Thus, in a river flow, the velocity at the bottom is practically non-zero. In theoretical studies of turbulent flow, the presence of a very thin boundary layer near the bottom is noted, in which the velocity sharply decreases to zero.

Turbulent motion is practically independent of fluid viscosity. The resistance to movement in turbulent flows is proportional to the square of the speed.

It has been experimentally established that the transition from laminar to turbulent and vice versa occurs at certain ratios between the velocity vav and the depth Hav of the flow. This relation is expressed by the dimensionless Reynolds number

the denominator (ν) is the coefficient of kinematic viscosity.

For open channels, the critical Reynolds numbers, at which the motion mode changes, vary approximately within 300-1200. If we take Re = 360 and the kinematic viscosity coefficient = 0.011, then at a depth of 10 cm the critical velocity (the speed at which laminar motion turns into turbulent) is 0.40 cm/s; at a depth of 100 cm, it decreases to 0.04 cm/s. Small values ​​of the critical velocity explain the turbulent nature of the movement of water in river flows.

According to modern concepts (A. V. Karaushev and others), elementary volumes of water (structural elements) with different sizes move inside a turbulent flow in different directions and with different relative velocities. Thus, along with the general movement of the stream, one can notice the movement of individual masses of water, leading, as it were, an independent existence for a short time. This, obviously, explains the appearance on the surface of a turbulent flow of small funnels - whirlpools, quickly appearing and disappearing just as quickly, as if dissolving in the total mass of water. This also explains not only the pulsation of velocities in the flow, but also the pulsations of turbidity, temperature, and the concentration of dissolved salts.

The turbulent nature of the movement of water in rivers causes the mixing of the water mass. The intensity of mixing increases with increasing flow velocity. The phenomenon of mixing is of great hydrological importance. It contributes to the alignment of the living section of the flow of temperature, concentration of suspended and dissolved particles.


Rice. 65. Examples of the curve of the water surface of the stream. a - screaming backwater, b - decline curve (according to A.V. Karaushev).

The movement of water in rivers

Water in rivers moves under the influence of gravity F'. This force can be decomposed into two components: Fx parallel to the bottom and F'y normal to the bottom (see Fig. 68). The force F' is balanced by the reaction force from the bottom. The force F'x, which depends on the slope, causes the movement of water in the stream. This force, acting constantly, should cause an acceleration of movement. This does not happen, since it is balanced by the resistance force arising in the flow as a result of internal friction between water particles and friction of the moving water mass against the bottom and shores. Changes in the slope, bottom roughness, narrowing and widening of the channel cause a change in the ratio of the driving force and the resistance force, which leads to a change in the flow velocities along the length of the river and in the living section.

The following types of water movement in streams are distinguished: 1) uniform, 2) uneven, 3) unsteady. With a uniform movement of the flow velocity, the free cross section, the water flow rate are constant along the length of the flow and do not change in time. This kind of movement can be observed in channels with a prismatic section.

With uneven movement, the slope, velocities, and free section do not change in a given section in time, but change along the length of the stream. This type of movement is observed in rivers during the low water period with stable water flow in them, as well as under conditions of backwater formed by a dam.

An unsteady motion is one in which all the hydraulic elements of the flow (slopes, velocities, open area) in the section under consideration change both in time and in length. Unsteady movement is typical for rivers during the passage of floods and floods.

With uniform motion, the slope of the flow surface I is equal to the bottom slope i and the water surface is parallel to the leveled bottom surface. Uneven movement can be slow and accelerated. With a slowing downstream flow, the curve of the free water surface takes the form of a backwater curve. The surface slope becomes less than the bottom slope (I< i), и глубина возрастает в направлении течения. При ускоряющемся течении кривая свободной поверхности потока называется кривой спада; глубина убывает вдоль потока, скорость и уклон возрастают (I >i) (Fig. 65).


Rice. 68. Scheme for the derivation of the Chezy equation (according to A. V. Karaushev).

Water flow rates and their distribution over the living section

The flow rates in rivers are not the same at different points in the flow: they vary both in depth and in the width of the living section. On each individual vertical, the lowest velocities are observed near the bottom, which is associated with the influence of the channel roughness. From the bottom to the surface, the increase in velocity first occurs rapidly, and then slows down, and the maximum in open streams is reached near the surface or at a distance of 0.2 H from the surface. Curves of vertical velocity changes are called hodographs or velocity diagrams (Fig. 66). The distribution of velocities along the vertical is greatly influenced by uneven bottom topography, ice cover, wind, and aquatic vegetation. If there are irregularities on the bottom (elevations, boulders), the speeds in the flow in front of the obstacle sharply decrease towards the bottom. The velocities in the near-bottom layer decrease with the development of aquatic vegetation, which significantly increases the roughness of the channel bottom. In winter, under the ice, especially in the presence of sludge, under the influence of additional friction on the rough lower surface of the ice, the velocities are low. The velocity maximum shifts towards the middle of the depth and is sometimes located closer to the bottom. Wind blowing in the direction of the current increases speed near the surface. With an inverse relationship between the wind direction and the current, the velocities near the surface decrease, and the position of the maximum shifts to a greater depth compared to its position in calm weather.

Along the width of the stream, both the surface and average velocities on the verticals change rather smoothly, basically repeating the distribution of depths in the open section: the velocity is lower near the coast, and it is the highest in the center of the stream. The line connecting the points on the surface of the river with the highest speeds is called the rod. Knowing the position of the rod is of great importance when using rivers for the purposes of water transport and timber rafting. A visual representation of the distribution of velocities in a living section can be obtained by constructing isototes - lines connecting points with equal velocities in a living section (Fig. 67). The area of ​​maximum velocities is usually located at some depth from the surface. The line connecting along the length of the flow the points of individual live sections with the highest speeds is called the dynamic axis of the flow.


Rice. 66. Diagrams of speeds. a - open channel, b - in front of the obstacle, c - ice cover, d - accumulation of sludge.

The average velocity on the vertical is calculated by dividing the area of ​​the velocity diagram by the depth of the vertical or in the presence of measured velocities at characteristic points in depth (VPOV, V0.2, V0.6, V0.8, VDON) using one of the empirical formulas, for example

Average speed in live section. Chezy formula

To calculate the average flow rate in the absence of direct measurements, the Chezy formula is widely used. It looks like this:

where Hav is the average depth.

The value of the coefficient C is not a constant value. It depends on the depth and roughness of the channel. There are several empirical formulas for determining C. Here are two of them:

Maning's formula

N. N. Pavlovsky's formula
where n is the roughness coefficient, is found according to the special tables of M. F. Sribny. The variable indicator in the Pavlovsky formula is determined by dependence.

It can be seen from the Chezy formula that the flow velocity increases with the hydraulic radius or mean depth. This is because with increasing depth, the effect of bottom roughness on the velocity value at individual points of the vertical decreases, and thereby the area on the velocity diagram occupied by low velocities decreases. An increase in the hydraulic radius also leads to an increase in the C coefficient. It follows from the Chezy formula that the flow velocity increases with an increase in the slope, but this increase in turbulent motion is less pronounced than in laminar one.

The speed of the flow of mountain and lowland rivers

The flow of lowland rivers is much calmer than mountain rivers. The water surface of lowland rivers is relatively flat. The obstacles are flowed around calmly, the backwater curve that occurs in front of the obstacle smoothly mates with the water surface of the upstream section.

Mountain rivers are characterized by extreme roughness of the water surface (foamy ridges, reverses, dips). Reverse faults occur in front of an obstacle (a heap of boulders at the bottom of the channel) or with a sharp decrease in the bottom slope. The surge of water in hydraulics is called a hydraulic (water) jump. It can be considered as a single wave that appeared on the water surface in front of the obstacle. The velocity of propagation of a single wave on the surface, as is known, c = , where g is the acceleration of gravity, H is the depth.

If the average flow velocity vav of the flow turns out to be equal to the wave propagation velocity or exceeds it, then the wave formed near the obstacle cannot propagate upstream and stops near the place of its excitation. A stopped wave of movement is formed.

Let vav = c. Substituting the value from the previous formula into this equality, we get vav = , or

The left side of this equation is known as the Froude number (Fr). This number makes it possible to estimate the conditions for the existence of a turbulent or calm flow regime: at Fr< 1 — спокойный режим, при Fr >1 - stormy mode.

Thus, the following relationships exist between the nature of the current, depth, speed, and, consequently, the slope: with an increase in the slope and speed and a decrease in depth at a given flow rate, the current becomes more turbulent; with a decrease in slope and speed and an increase in depth at a given flow rate, the flow becomes more calm.

Mountain rivers are characterized, as a rule, by a rapid flow, lowland rivers have a calm flow regime. A turbulent flow regime can also occur in the rapids of lowland rivers. The transition to a turbulent flow sharply increases the turbulence of the flow.

Transverse circulations

One of the features of the movement of water in rivers is the non-parallel jet of currents. It is clearly manifested on roundings and is observed on straight sections of rivers. Along with the general movement of the flow parallel to the banks, there are in general internal currents in the flow directed at different angles to the axis of movement of the flow and producing movements of water masses in a direction transverse to the flow. At the end of the last century, the Russian researcher N. S. Lelyavsky drew attention to this. He explained the structure of internal currents as follows. On the rod, due to high velocities on the water surface, jets are drawn in from the side, as a result, a certain level increase is created in the center of the flow. As a result, in a plane perpendicular to the direction of flow, two circulation flows are formed along closed contours, diverging near the bottom (Fig. 69 a). In combination with translational motion, these transverse circulation currents take the form of helical motions. The surface current directed to the rod, Lelyavsky called faulty, and the bottom divergent - fan-shaped.

On curved sections of the channel, water jets, meeting with a concave shore, are thrown away from it. The masses of water carried by these reflected jets, which have lower velocities, are superimposed on the masses of water carried by the following jets running on them, and raise the level of the water surface near the concave shore. As a result, a skew of the water surface occurs, and water jets located near the concave shore descend along its slope and are directed in the bottom layers to the opposite convex shore. There is a circulation flow in the curved sections of the rivers (Fig. 69 b).


Rice. 69. Circulation currents on a straight (a) and on a curved (b) section of the channel (according to N. S. Lelyavsky). 1 - plan of surface and bottom jets, 2 - circulation currents in the vertical plane, 3 - helical currents.

Features of the internal flows of the flow were studied by A. I. Losievskii in laboratory conditions. He established the dependence of the form of circulation currents on the ratio of the depth and width of the flow, and distinguished four types of internal currents (Fig. 70).

Types I and II are represented by two symmetrical circulations. Type I is characterized by jet convergence near the surface and diverging near the bottom. This case is characteristic of watercourses with a wide and shallow channel, when the influence of the banks on the flow is insignificant. In the second case, the bottom jets are directed from the coast to the middle. This type of circulation is typical for deep flows with high velocities. Type III with one-way circulation is observed in triangular channels. Type IV - intermediate - can occur during the transition from type I to type II. In this case, the jets in the middle of the flow can be converging or diverging, respectively, near the coast - diverging or converging. The concept of circulation currents was further developed in the works of M. A. Velikanov, V. M. Makkaveev, A. V. Karaushev, and others. Theoretical studies of the origin of these currents are presented in special courses on hydraulics and the dynamics of channel flows. The appearance of transverse currents on the curvature of the channel is explained by the centrifugal force of inertia developing here and the transverse slope of the water surface associated with it. The centrifugal force of inertia that occurs on roundings is not the same at different depths.


Rice. 70. Scheme of internal currents (according to A. I. Losievsky). 1 - surface jet, 2 - bottom jet.

Rice. 71. Scheme of the addition of forces that cause circulation. a — vertical change of the centrifugal force P1, b — overpressure, c — resulting diagram of the centrifugal and overpressure forces acting on the vertical, d — transverse circulation.
At the surface it is greater, at the bottom it is less due to a decrease in the longitudinal velocity with depth (Fig. 71 a).

Depending on the direction of the bend, the deflecting Coriolis force either strengthens or weakens the transverse currents on the rounding. The same force excites transverse currents in straight sections.

At low levels on the rounding, circulation currents are almost not expressed. With increasing levels, increasing speed and centrifugal force, circulation currents become distinct. The velocity of transverse currents is usually small - ten times less than the longitudinal component of the velocity. The described nature of the circulation currents is observed before the water reaches the floodplain. From the moment the water enters the floodplain, two streams are created in the river - the upper one, in the valley direction, and the lower one, in the root channel. The interaction of these flows is complex and little studied.

In modern literature on the dynamics of channel flows (K. V. Grishanin, 1969), apparently, a more rigorous explanation is given for the occurrence of transverse circulations in a river flow. The origin of such circulations is associated with the mechanism of transmission to the elementary volumes of water in the flow of the action of Coriolis acceleration by means of a pressure gradient caused4 by the transverse slope (and constant on the vertical), and the difference in shear stresses caused on the faces of elementary volumes of water by differences in the flow velocities along the vertical.

A role analogous to Coriolis acceleration is played by centripetal acceleration at the turn of the channel.

In addition to transverse circulation, vortex motions with a vertical axis of rotation are observed in the flow (Fig. 72).


Rice. 72. Scheme of vortices with vertical axes (according to K. V. Grishanin).

Some of them are mobile and unstable, others are stationary and have large transverse dimensions. More often they occur at the confluence of streams, behind steep bank ledges, when flowing around certain underwater obstacles, etc. The conditions for the formation of stationary eddies have not yet been studied. Grishanin suggests that the formation of a stable localized vortex is facilitated by a significant depth of the flow and the existence of an upward flow of water. These whirlwinds in the flow, known as whirlpools, resemble air whirlwinds - tornadoes.

Transverse circulations, eddy movements play an important role in the transport of sediments and the formation of river channels.