How come rivers that are narrow are faster than rivers that are wide? Is there science behind it?

Question

I've become very curious about this stuff and I want to know the science behind the speed of rivers, I mean if you had 2 streams with only size differences, how does that manipulate speed? People are saying that water is incompressible so I'm VERY confused, thank you in advanced

Answer 1

Instead of thinking about 2 streams, think of one stream with vaying width. Let the wide section be upstream of the narrow section. In 1 second, a certain volume of water passes rock #1 which is in the wide section. That water continues downstream where the stream gets narrow and has rock #2 in the middle. If the water ran at the same speed, the same volume of water could not pass rock (#2) in 1 second. So what would happen? Water would pile up in a flood upstream of the narrow section. That would force the flow in the wide section to get even slower. That's not what would happen. The water flows faster in the narrow section to get that same volume past rock #2.



The units of flow rate in a river are cubic meters/second. That number has to be equal in any part of the river. (Unless some other river joins the river bringing extra water into the situation.)

Answer 2

Its a matter of passing an equivalent volume of water.

So it should be obvious that because the cross sectional area of a narrow stream can be much smaller than a wide one, it must run faster in the narrow one to deliver the same volume.

Answer 3

This is due to what is known as the "Venturi effect", where pressure decreases and the velocity of a fluid increases, this is a special case of Bernoulli's theorem, where the height of the fluid, while choosing a choice of axes to make the height zero, we can equate the total head (which is the amount of energy corresponding to a static fluid in a column of water corresponding to it's height) which equals to the sum of the total kinetic energy of unit volume plus the total potential energy of unit volume + pressure= a constant, due to conservation of energy, and thus we can set the total potential energy to zero, assuming that since the total head does not change, so as the velocity increases, the pressure must decrease.





Also, what people mean when water is an incompressible fluid, is when you subject water to a pressure of 1 atmosphere, it only changes in volume by 1/2000 of it's original volume, I hope my answers cleared up your confusions.

Answer 4

Water density is a constant. This make Area*cross section (height*breadth)=constant.

We can say narrower the size faster is the velocity.

Answer 5

It's like running to same amount of water through two pipes. One is thin, the other thick. There will be more pressure in the smaller pipe