Flow of widening river

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Experimental procedure and explanation:

• How does the speed change in a river as the flow becomes wider downstream?
• Let’s conduct an experiment with a flow channel that becomes wider partway. When finely-shredded paper is floated on the water surface and allowed to flow, it slows down as the flow widens.
• The cross-sectional area of the flow channel is larger in the downstream side than in the upstream side. Hence, the flow speed becomes decreases.
• The flow speed is inversely proportional to the cross-sectional area of the flow channel. When we multiply the average speed of the flow (calculated within the cross-sectional area) with the cross-sectional area of the channel, we get the flow rate. Another way to look at it is that the flow rate is constant for both the upstream and downstream sides, which is the volume of fluid passing through per second.
  (flow rate) = (flow channel cross-sectional area) × (average flow speed) = equivalent upstream and downstream.
  This is called the continuity equation.
• Therefore, the flow rate is higher in narrow rivers and lower in wider rivers.
• (Supplement) When conducting this experiment, it is important to widen the flow channel gradually. A sudden widening of the flow channel can cause the flow from upstream to concentrate on one section, leaving the surrounding water to flow slowly or even backwards in some cases. This phenomenon is called “separation”.
• This video of the experiment was produced with the support of JSPS KAKENHI 18K03956.

[Keywords]	Expansion flow, continuity equation
[Related items]	Flow of narrowing river
[Reference]	“Illustrated Fluid Dynamics Trivia,” by Ryozo Ishiwata, Natsume Publishing, p. 190–191. “The Wonders of Flow,” Japan Society of Mechanical Engineering, Kodansha Blue Backs, p. 151–152.

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