Speed of flow in a curved river 2

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What type of experiment is this?

Experimental procedure and explanation:

• The flow of a curved river is taught in 5th-grade science. These textbooks state (as of academic year 2018) that “flows are fast on the outer side and slow on the inner side of curves”; however, it has been observed that this is not always the case in some experiments because the behavior of a curved flow is typically opposite to what is written in textbooks and “flows are slow on the outer side and fast on the inner side of curves” (this is a basic concept in fluid dynamics). Therefore, when conducting this experiment under normal circumstances, the results are often opposite to what is written in textbooks. Let’s confirm this phenomenon. The following experiment is conducted with a constant water depth. An actual river is influenced by water depth or river bed undulations; supplementary explanations are given in [Advanced] (the explanation below is almost identical to that in the previously published “Speed of flow in a curved river” ).
• To observe the flow of the curve, modifications were made to the experimental tools used in the “Speed of flow in a curved river” experiment. A 90 cm long, 60 cm wide, and 5 cm thick urethane foam board was used as the base of the device, and a 12 cm-wide flow channel was created by attaching a 5 cm-thick urethane foam board on top of it. The edge of the flow channel was sealed with a filler commonly used in bathtubs. A submersible pump with an output of around 40 L/min was used to generate the flow. The water level in the flow channel was maintained by placing a rectifier with bundles of straws (diameter 4.5 mm, length 6 cm) on the upstream side and attaching a 2.5 cm-high partition plate with multiple 5 mm-diameter holes (made using a hole punch) on the outlet side.
• When shredded paper is floated on the water surface, it can be observed that the paper flows slower on the outer side and faster on the inner side in a curved river—a common observation when the water depth is constant.
• When water flows in a straight path and hits the sides on the outer side, it increases the pressure on that side. This pressure difference with the inner side, which has comparatively lower pressure, results in water curving toward the inner side, generating centripetal acceleration, and curving along the river.
• As the flow on the outer side approaches the curve, it moves toward the high-pressure section and gradually decelerates, thereby slowing down. To maintain the overall flow rate, the flow on the inner side must become faster to compensate for the slower flow on the outer side.
• To be more specific, as the flow on the outer side of the curve approaches, it experiences an increase in pressure energy, which causes a decrease in kinetic energy and leads to deceleration. To compensate for this decrease in flow rate, the flow on the inner side must become faster because, on the inner side, the pressure energy decreases and the kinetic energy increases, causing an increase in flow speed. This results in the flow being slower on the outer side and faster on the inner side of the curve. This flow can be considered as part of a swirling flow, and if the effects of viscous friction are ignored, it can be modeled as a free vortex. In such a model, the peripheral speed increases inversely proportional to the radius from the center of the circle.
• It can be observed from this experiment that the effect of curving is that the flow becomes “slower on the outer side, and faster on the inner side”. This is a basic concept in fluid mechanics. This is the reason that some experiments do not work well. A supplementary explanation of the effects of water depth and other factors on actual rivers is given in [Advanced]
• This video of the experiment was produced with the support of JSPS KAKENHI 18K03956.

[Advanced]	The basic concept for flow in a curve is “slower on the outer side and faster on the inner side.” However, in an actual river, various influences such as the water depth, topography, river bed undulations, secondary flow (explained in “Secondary flow and sediment in curved river”), and separation may form an area where “flows are fast on the outer side and slow on the inner side”. In actual rivers, sediment deposition usually occurs on the inner side of the river, which makes it shallower and slows down the flow. On the other hand, the flow is often faster in the center and on the outer side of the river width. However, the effect of viscosity on the deceleration in the shallow water area is generally small, unless the water is very shallow. Moreover, irregularities in the river bed can also influence the flow speed at each location. Therefore, whether the outer or inner side of a river is faster depends on the specific characteristics of each river. Additionally, the latter half of the curve may also slow down the flow on the inner side due to the effect of secondary flow. Another reason for flow deceleration (and sometimes separation)is the rise in pressure from low pressure to the original pressure on the inner side near the end of the curve. Details are explained in the  [Advanced] in “Secondary flow and sediment in curved river”.
[Keywords]	Swirling flow, free vortex
[Related items]	Speed of flow in a curved river, Free vortex and forced vortex, Secondary flow and sediment in curved river
[Reference]	“The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, p. 52–59.

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