Speed of Flow in a Curved River

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What type of experiment is this?

Experimental procedure and explanation:

• Using the same model that we used for “Speed of Flow in a Straight River,” we observed the flow at a bend in the river.
• In this experiment, the water flows slowly on the outside of the bend, and faster on the inside of the bend. In general, these flow speed characteristics hold true if the water depth is constant.
• When the flow of water that has been going in a straight line hits the outer side, the pressure on the outer side increases. The water curves inwards because of the difference between the lower pressure on the inside and the higher pressure on the outside, in a phenomenon called centripetal acceleration, and this is how the water flows downstream.
• Ignoring the effects of viscous friction and so on, the potential energy due to pressure increases at the outside of the bend, and the kinetic energy decreases by that amount as the flow slows down. However, at the inside of the bend, the kinetic energy increases by the amount that the potential energy due to pressure decreases as the flow speeds up. This is why the flow is slower at the outside of the bend and faster at the inside of the bend. This can be thought of as part of a swirl flow, and if we ignore the effects of viscous friction and so on, the situation is exactly the same as a free vortex: the peripheral speed is inversely proportional to the radius from the center of the circle, and therefore the flow’s speed increases with decreasing distance from the inside of the bend.
• In an actual river, the speed relationship described above may change because the speed is affected by various factors including topography, water depth, rocks, and viscous friction with the bottom of the river. Nonetheless, the basic flow state is that the flow is slower on the outside and faster on the inside, as explained above, and then the flow changes in response to other factors.

[Keywords]	Swirl flow, Free vortex
[Related items]	Speed of Flow in a Straight River, Free Vortex and Forced Vortex
[Reference]	“The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, P52・・9.