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Classical Mechanics Level 1

Water in a river speeds up as it goes over the top of a waterfall. What is the primary reason this happens?

The water molecules separate which leads to less viscosity. The waterfall is closer to the earth, so the force of gravity is stronger. Nature just likes to be pretty. The net force on the water increases as the water reaches the top of the falls.

4 solutions

Ananthakrishnan Aj
Jun 29, 2014

The river water is only accelerated by the sine component of gravity while flowing.Therefore the flow velocity will be mainly determined by the angle of depression of the land. But as it flows over the top the entire gravitational force starts to act on the water as the depression angle increases to 90 degrees. Thus the water experiences a sudden increase of velocity.

Note: The flow will also depend upon the depth and width of the river according to the equation of continuity.But for the current question we consider these as constants.

But gravity will also pull the water???????

Anuj Shikarkhane - 6 years, 11 months ago

I think that the answer lies in the principle of Bernoulli's Theorem. At more height, water has more potential than kinetic energy and as they come down, due to the height difference, the potential energy of the water gets converted into kinetic energy.

Suraj Subraveti - 6 years, 11 months ago

Nope. Bernoullli's theorem states that liquid when encounters obstacle in the flow, such is the rock in the river, all molecules of the liquid will reach the end point at same time. To satisfy this condition, molecules that travel longer distance will travel faster and also creating less pressure on same side. That is why the cross sectional shape of the airplane is tear drop with longer surface on the top. Some source .

Dervis Mahmutcehajic - 6 years, 11 months ago

Clay Young
Jul 4, 2014

Aj stated the answer but in a way incomprehensible to the common person. "Sine component of gravity"!? A simpler way of looking at it is that the river has nothing holding it in at the fall so the water moves toward it, being pushed by the water behind it.

Revanth E K
Jun 29, 2014

potential energy changes to kinetic energy .as we know when the a body at a greater height falls to lower height their is a conversion preserving energy hence PE changes to KE..........

This above is the most correctly formulated answer, in my opinion. Actualy, "correct" answer is wrong - there is no raise in forces, but a sort of 'recomposition' of forces. For a common person - 'lack of resistance' in the zone close to edge. Most formulations which tend to simplify the explanation for a person who doesn't really get some basic principles of energy and mass conservation very often lead to complete misunderstanding of very basic things. That's why I have picked the "wrong" answer, not even sure what the heck was the relation between the question and any of answers offered.

Zoran Radošević - 5 years, 5 months ago

Lucas Franceschi
Jul 29, 2014

A simple way of thinking about this is that the water molecules that are dropping in the waterfall simply for not having ground anymore are being pulled away from the ones behind it, and since they are all "bound" to each other they pull with them those behind them, so that, if you look at a single molecule, it will first be pulled by the ones falling, then it will start falling and will pull with it the ones still behind. Clever! never stopped to think about it :D

You can also think about the fact that the molecules that are accelerating (because they are falling) leave an empty space behind them to which the other molecules will be pulled by the difference of pressure. It's the same principle that forms vortices in the water when you move your hand in it, for instance.

This is also very, very good common explanation!

Zoran Radošević - 5 years, 5 months ago

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