The more water that has to pass through a passage in a certain time, the faster the current is. This is the case, for example, with the tap of the water supply system. The further you open the tap, the faster the water flows. More water flows through the pipe and through the tap per time unit.

If you made a cross-section of a straight section of the river, you’d notice that the water particles move faster in one place than in another. In general, on a straight section of the river in the middle, the water will flow fastest.

Figure 6: Approximately at the cross the water will flow the fastest

Figure 7 shows the behaviour of the water particles in a bend of a river.

Figure 7: Top view of the (upper) stream in a bend
  • The current comes from C.
  • The water particles want to go straight ahead.
  • The trajectory of the water particles is deflected by the shore.
  • The current is concentrated along the bank on the side of A (because of the “hang”).

As a result, the current at A is stronger than at C and the current at B is less strong than at C.
The cross-section of this bend will look like the following picture: on the side of A the bottom has been sanded out, on the side of B the transported material has sunk.

Figure 8: Diameter of the bend

In addition to the (upper) current already discussed, there is also a so-called undercurrent in the river. This stream runs like a spiral through the river. The figure below shows the undercurrent and upstream current. We’ll come back to this in the navigation section.

………. under current

_____  upper current

Figure 8a: Under current and upper current

We have already noted that the flow rate on a river is not constant and is not the same on the entire river. The flow rate depends on:

  • the slope of the river bottom;
  • the quantity of water supplied;
  • the depth and width of the river;
  • the influence of low and high tide.

The slope of a river bottom

The bottom of a river is not flat. The river has to bridge a great hight from its origin to its outlet into the sea. For example, the bottom of the Rhine is higher in Germany than in the Netherlands. In Germany, the height difference of the river bottom is also greater than in the Netherlands.

When someone says: “The decline between A and B is 10 metres”, so the difference in height between A and B is 10 metres.

The decline is the difference in height between two points along a river.

However, it makes quite a difference whether A and B are 10 kilometres apart or 100 kilometres. In the first case the slope is much steeper than in the second case. The current will therefore be much stronger in the first case than in the second.

In addition to the amount of surface water, the current also depends on the gradient of the river.

The gradient on the river is the number of metres you go up per kilometre, or how many kilometres you have to sail to go up by 1 metre.

In order to determine this so-called gradient, it is not enough to know the extent of the decline between point A and B. A captain must therefore know the distance between these two points. Then the gradient can be calculated. The formula is as follows:

Gradients is: decline : distance

Above the line is always 1 metre. This metre shows the decline. Below the line the number of metres a ship has to sail to go up or down 1 metre.

An example:

1 metre : 10,000 metre

This means: a captain has to sail 10,000 metres or 10 km to overcome 1 metre of difference in height.

An example from practice:

Between Lobith and Dodewaard the river bottom descends 4.05 m. So the decline is 4.05 m.

The distance between Lobith and Dodewaard is 33.8 km. The gradient on that part of the river:

4.05 m : 33.8 m or 4.05 m : 33,800 m

But we have to make sure that above the line is 1 metre. An additional calculation must be made. 4.05 metres is therefore divided by 4.05 metres, which comes to 1 metre. To get the fracture right, we also have to divide 33,800 m by 4.05, which comes to 8345 metres. The completed formula:

1 m : 8.345 km or 1 : 8345

The “m” for metres is usually left out. This means that in order to bridge a height difference of 1 metre, the ship has to sail an average of 8345 metres on this section of the river. In other words, every 8.345 km the bottom descends or rises 1 metre.

In a drawing this looks like this:

Figure 9: Gradient

Along the river there are signs indicating the mileage (kmr). The indicated kilometres are calculated from the origin of the river. The signs along the Rhine indicate the distance from Lake Constance. The distance between two places can be deduced from these kilometres.

As you can see, the amount of water in the river depends on the catchment area. This quantity affects the regime of a river. As an example, we give the Rhine and the Meuse.

The amount of water supplied

The Rhine with a catchment area of about 185,000 km² is mainly a glacier river, so the water discharge close to its origin is fairly constant. The regular discharge of the river is reinforced by the presence of Lake Constance. This lake, which is 60 km long and 25 km wide, is close to its origins and has a strong regulatory character for the Rhine. Because of the large dimensions of this lake it is able to collect the sometimes excessive amount of meltwater and it is discharged more gradually than if this collection would not be present. As a result, downstream flooding is generally prevented.

In other parts of the Rhine, outlet can be very different. This is due to precipitation from the various tributaries (the catchment area). This precipitation can be very local, which means that the outlet and the water level can vary from place to place and from day to day. Normally at Lobith-Tolkamer an average of 2200 m³ of water per second flows into our country. However, due to fluctuating water discharge from the catchment area, this can vary from 750 m³  to 13000 m³ per second.

The discharge of the Meuse, with a catchment area of about 33,000 km²; the Meuse fluctuates more strongly than the Rhine. In the past, in the summer months, the discharge could become so low that parts of the Meuse upstream of Maasbracht could even become fordable. However, in the event of heavy precipitation or sudden thaw, very high water levels can occur, with the Meuse flooding large parts of Limburg. These high water levels often occur in the winter months.

The high water levels on the Dutch Meuse are mainly caused by the rivers in the Ardennes such as the Semois, Lesse, Outhe, Sambre and other rivers and streams that drain into the Meuse. Because of the rocky soil, the narrow brook valleys and the great decline of the mountain streams in the Ardennes, the precipitation is very quickly transported to the Meuse. To increase the navigability of the Meuse and to combat high water, seven weirs were built in the Meuse between 1920 and 1930, with lock complexes linked to them. Between Borgharen and Stevensweert (Grensmaas) the Meuse has no weir.

Because Belgium and the Netherlands could not agree on the construction of this part of the Meuse, in the years 1920-1930 parallel to this part of the Meuse and canal was constructed, the Juliana Canal. The Juliana Canal is 32 kilometres long and has a drop of approximately 22.5 metres. This decline has been overcome by the lock complexes of Born (11 metres) and Maasbracht (11.5 metres). Near Limmel there is a lock that is open most of the year. This lock is only in operation when there are high discharges of the Meuse.

Depth and width of a river

In places where the river is narrow, the current will increase significantly. A well-known example is  still the Binger Loch in the Rhine. All the water that comes from the source must come from a wide river here through a narrow passageway. This will greatly increase the flow rate. In the Netherlands, too, the flow velocity will increase as the above-water level increases until the floodplains are flooded. At that moment the water spreads and the flow rate will decrease significantly.

Influence of ebb and flow

On rivers where low and high tide are noticeable, the current is also variable. At low tide the upper water can go to sea more easily and the current can be maximum at that location. At high tide, the surface water is hindered by the outside water. The limit at which low and high tide are noticeable also depends on the amount of surface water. At an average discharge at Lobith, a rule of thumb is that the flood current is noticeable up to Gorkum, and at the Lek, the flood current is noticeable up to Vreeswijk.