Fording a river physics question

Sac Arrow

Sac Arrow

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Snorting his way across the USA
Let's say you have a non-equatorial river flowing due south in the northern hemisphere.

Which side of the river will be higher than the other?

Why?
 
Exploring Coriolis forces today? Things moving in the northern hemisphere feel a Coriolis force to the right. So a southbound river will be pushed a little to the west...

...Or, are you talking about how the rate of rotation of the Earth is changing very slowly, so there's an angular acceleration? That would cause some sloshing too. Unfortunately, I left my Randall Munroe book (that talks about this) at home, so I don't remember which way it goes, whether we're speeding up or slowing down.

Edit: I guess we're also assuming that the river has no bends, has zero curvature to its direction of flow, right? Also in a vacuum. :)
 
The Coriolis Effect acts on the water of the river. The strongest erosion will be on the right (west) side of the river because the effect slightly enhances water velocity. Albert Einstein was not the first to observe this, but he did write a paper on the topic.
 
Sac Arrow said:
Let's say you have a non-equatorial river flowing due south in the northern hemisphere.

Which side of the river will be higher than the other?

Why?
Click to expand...
In the Northern hemisphere a southward flow of air or water will bend to the right due to Coriolis force. Its eastward inertia due to the earth's rotation means that flowing from a higher latitude to a lower one also extends its radius from the center of the earth's rotation, so it slows its eastward flow (conservation of momentum) and appears to bend to the west to accomodate its inertia in space. That will make a straight river higher on the west bank.

Any curve in the river will put the water higher on the outside of the curve due to centrifugal force, which is more powerful than Corilis force.

I think.
 
kath said:
Exploring Coriolis forces today? Things moving in the northern hemisphere feel a Coriolis force to the right. So a southbound river will be pushed a little to the west...

...Or, are you talking about how the rate of rotation of the Earth is changing very slowly, so there's an angular acceleration? That would cause some sloshing too. Unfortunately, I left my Randall Munroe book (that talks about this) at home, so I don't remember which way it goes, whether we're speeding up or slowing down.

Edit: I guess we're also assuming that the river has no bends, has zero curvature to its direction of flow, right? Also in a vacuum. :)
Click to expand...

That's right. And I'm leaving Eotvos out of the mix today. You're the right person to ask - can, in theory, the Corolis force influence the direction water swirls draining from a tank?
 
Sac Arrow said:
That's right. And I'm leaving Eotvos out of the mix today. You're the right person to ask - can, in theory, the Corolis force influence the direction water swirls draining from a tank?
Click to expand...

Yes. *If* the tank is a) very big, and b) very still water, before you c) very delicately pull the plug. (So, a myth for toilets and sinks.).
"Veritasium" did a great YouTube video demonstrating this, but had to go to rather extraordinary lengths to see the tiny effect.

But hey, I'm in Australia right now. So if you need me to test anything, let me know. :)

Edit: the "Veritasium" guy did the experiment in the Southern Hemisphere, while the "Smarter Every Day" guy did the exact same experiment in the Northern Hemisphere... the two videos are designed to be "synced" to each other and watched together:
http://www.smartereveryday.com/toiletswirl
 
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kath said:
Yes. *If* the tank is a) very big, and b) very still water, before you c) very delicately pull the plug. "Veritasium" did a great video demonstrating this, but had to go to rather extraordinary lengths to see the tiny effect.

But hey, I'm in Australia right now. So if you need me to test anything, let me know. :)
Click to expand...

Well okay but is it actually due to the Coriolis effect (remember the tank isn't moving) or a rotational acceleration?
 
Dan Thomas said:
In the Northern hemisphere a southward flow of air or water will bend to the right due to Coriolis force. Its eastward inertia due to the earth's rotation means that flowing from a higher latitude to a lower one also extends its radius from the center of the earth's rotation, so it slows its eastward flow (conservation of momentum) and appears to bend to the west to accomodate its inertia in space. That will make a straight river higher on the west bank.

Any curve in the river will put the water higher on the outside of the curve due to centrifugal force, which is more powerful than Corilis force.

I think.
Click to expand...

Is the higher on the east or west? I (inexpertly) thought it eroded more on the west bank because the water coming into the west bank had the addition of the downstream current where as the east bank would have a lower velocity water hitting it because it had to come upstream first

But what do I know? I can't keep barometer / altitude / altimeter questions straight either.
 
Depends on too many factors to provide a correct answer.
 
Sac Arrow said:
Well okay but is it actually due to the Coriolis effect (remember the tank isn't moving) or a rotational acceleration?
Click to expand...
Corilois force is very small and is only apparent on a larger scale. The water in a sink or toilet bowl is much more affected by imperfections in the shape of that bowl than by any Coriolis forces.
 
Dan Thomas said:
Corilois force is very small and is only apparent on a larger scale. The water in a sink or toilet bowl is much more affected by imperfections in the shape of that bowl than by any Coriolis forces.
Click to expand...

Right, but the question at hand is whether any directional bias that is present is due to the Coriolis force, or some other rotational dynamic of the Earth. The Coriolis force is not present on a stationary object, specifically, an object not travelling in the north or south direction or some component thereof.

Let's look at two cases: First, the poles. The Coriolis force is strongest at the poles and zero at the equator. Let's put our tank on the axis of rotation, and allow the water to stabilize and achieve rotational inertia so it is not moving inside the tank. There should be no force acting on it that would cause it to swirl in one direction or the other. Second, the equator. Same thing. It's like slinging a bucket of water on a rope.

But, move out of plane, and not only are you rotating the tank, but you are wobbling it back and forth as well as it rotates around the earth. Now that should cause a small degree of acceleration of the water within the tank.
 
Sac Arrow said:
Right, but the question at hand is whether any directional bias that is present is due to the Coriolis force, or some other rotational dynamic of the Earth. The Coriolis force is not present on a stationary object, specifically, an object not travelling in the north or south direction or some component thereof.
Click to expand...

Right... almost. The Coriolis Force will show up anytime an object has a velocity ("v") that has a component perpendicular to the vector sticking out the axis of the North Pole (what physicists call the "omega" or angular-velocity vector). So moving in any direction* (north, south, east, or west) there will be some perpendicular component between the two. F goes as -(omega-cross-v), for the math nerds.
So yes, if the water is stationary in the tank, there is no Coriolis effect; it only shows up if the water is flowing. The "v" in the equations refers to the velocity of the water within the tank relative to the Earth, not the tank itself; the tank is presumed fixed to the spinning Earth. Or there doesn't need to be a tank at all (as with global air masses and currents).

*... Except at the equator, where if you move due north the "v" vector and the "omega" vector are parallel. Technically, if you move east or west at the equator, there *is* a Coriolis Force but it will point straight into or out of the Earth, and so you won't feel it as a "sideways" pull like at other latitudes. Depending on your latitude and what direction you're moving, some component of the fictitious** force vector may point into or out of the sky, and people usually don't count that as part of the "Coriolis Effect" that makes things swirl/pull sideways. [All of this is easier if you get a basketball and use the fingers of your right hand (locked in the "right-hand-rule position") to figure out some vector cross-products!]. But in any case, for the slowly-spinning Earth, it's a very small effect, way too small to make a difference in a sink or a toilet, as others have said...

** The Coriolis and Centrifugal forces are called "fictitious" forces because they are not really pushes or pulls from anything, but just the consequences of living in a rotating reference frame (in our case the spinning Earth).

I was being just a bit facetious about the "Earth spinning up/slowing down" angular acceleration thing... that effect is truly tiny, probably not even measurable. But if Earth did have a sizable angular acceleration, it would create all kinds of additional fictitious forces (besides just our two favorites, the Centrifugal and the Coriolis), and the world would be an interesting place. But that's a different topic. :)


P.S. I watched the Aussie toilet here carefully, and it was mostly just a roil of chaos... but if there was any rotation to the flush, it looked CCW (Northern-style) to me.
I'm still pretty jet lagged.
 
Can a truck driver carrying a load of Geese in an enclosed container lighten his load and make it across a bridge that he's otherwise too heavy to cross?
 
Sac Arrow said:
Right, but the question at hand is whether any directional bias that is present is due to the Coriolis force, or some other rotational dynamic of the Earth. The Coriolis force is not present on a stationary object, specifically, an object not travelling in the north or south direction or some component thereof.

Let's look at two cases: First, the poles. The Coriolis force is strongest at the poles and zero at the equator. Let's put our tank on the axis of rotation, and allow the water to stabilize and achieve rotational inertia so it is not moving inside the tank. There should be no force acting on it that would cause it to swirl in one direction or the other. Second, the equator. Same thing. It's like slinging a bucket of water on a rope.

But, move out of plane, and not only are you rotating the tank, but you are wobbling it back and forth as well as it rotates around the earth. Now that should cause a small degree of acceleration of the water within the tank.
Click to expand...

It will cause a small rotational force, alright, but not enough to overcome the disturbances to the flow caused by imperfections in the bowl's shape or roughness, or inside the drain tube that will inevitable have some tiny tendency to start the flow rotating. The toilet bowl's inlet holes under the rim are notoriously crude nozzles, too, and will usually impart some swirl to the water. The Coriolis force across a 12-inch bowl will be extremely tiny, especially considering the very low velocity of the water across the bowl as it drains. https://www.washingtonpost.com/news...rove-once-and-for-all-which-way-water-swirls/
 
Tantalum said:
Can a truck driver carrying a load of Geese in an enclosed container lighten his load and make it across a bridge that he's otherwise too heavy to cross?
Click to expand...
If the truck drives on a treadmill on the bridge...
 
Tantalum said:
Can a truck driver carrying a load of Geese in an enclosed container lighten his load and make it across a bridge that he's otherwise too heavy to cross?
Click to expand...
Nope.
The air pressure will be higher on the bottom of the container and generate a net downward force equal to the weight of the geese.

The laws of physics may be blithely ignored by the FAA and it's minions, but in the real world, they will not be denied.
 
kath said:
Right... almost. The Coriolis Force will show up anytime an object has a velocity ("v") that has a component perpendicular to the vector sticking out the axis of the North Pole (what physicists call the "omega" or angular-velocity vector). So moving in any direction* (north, south, east, or west) there will be some perpendicular component between the two. F goes as -(omega-cross-v), for the math nerds.
So yes, if the water is stationary in the tank, there is no Coriolis effect; it only shows up if the water is flowing. The "v" in the equations refers to the velocity of the water within the tank relative to the Earth, not the tank itself; the tank is presumed fixed to the spinning Earth. Or there doesn't need to be a tank at all (as with global air masses and currents).

*... Except at the equator, where if you move due north the "v" vector and the "omega" vector are parallel. Technically, if you move east or west at the equator, there *is* a Coriolis Force but it will point straight into or out of the Earth, and so you won't feel it as a "sideways" pull like at other latitudes. Depending on your latitude and what direction you're moving, some component of the fictitious** force vector may point into or out of the sky, and people usually don't count that as part of the "Coriolis Effect" that makes things swirl/pull sideways. [All of this is easier if you get a basketball and use the fingers of your right hand (locked in the "right-hand-rule position") to figure out some vector cross-products!]. But in any case, for the slowly-spinning Earth, it's a very small effect, way too small to make a difference in a sink or a toilet, as others have said...

** The Coriolis and Centrifugal forces are called "fictitious" forces because they are not really pushes or pulls from anything, but just the consequences of living in a rotating reference frame (in our case the spinning Earth).

I was being just a bit facetious about the "Earth spinning up/slowing down" angular acceleration thing... that effect is truly tiny, probably not even measurable. But if Earth did have a sizable angular acceleration, it would create all kinds of additional fictitious forces (besides just our two favorites, the Centrifugal and the Coriolis), and the world would be an interesting place. But that's a different topic. :)


P.S. I watched the Aussie toilet here carefully, and it was mostly just a roil of chaos... but if there was any rotation to the flush, it looked CCW (Northern-style) to me.
I'm still pretty jet lagged.
Click to expand...

But I -think- the Eotvos effect is considered to be separate from Coriolis. Coriolis contemplated lateral acceleration/force due to north-south movement, whereas Eotvos contemplated the centripetal component.

Eotvos was the Hungarian physicist who was the first to be able to measure an apparent change in gravity due to travel in the east-west direction. He placed accelerometers, which were basically heavy masses suspended by a spring, which recorded their own weight, on ships. He was able to show that the ships traveling east appeared to weigh slightly less than those traveling west, by the amount one would calculate to be the case due to centripetal force offset.

The Germans first tried experiments in WWI by firing artillery shells to the east and west. In theory, those fired east should travel further. They couldn't find a difference within the accuracy of the guns, however.

Dan Thomas said:
It will cause a small rotational force, alright, but not enough to overcome the disturbances to the flow caused by imperfections in the bowl's shape or roughness, or inside the drain tube that will inevitable have some tiny tendency to start the flow rotating. The toilet bowl's inlet holes under the rim are notoriously crude nozzles, too, and will usually impart some swirl to the water. The Coriolis force across a 12-inch bowl will be extremely tiny, especially considering the very low velocity of the water across the bowl as it drains. https://www.washingtonpost.com/news...rove-once-and-for-all-which-way-water-swirls/
Click to expand...

I don't take issue with the fact that whatever rotational force is there is fairly insignificant. My argument is more with semantics, as to whether it is actually due to the Coriolis effect. As Kath has pointed out, The Coriolis force won't be present when the water is at a still state. That will obviously change when the water starts swirling.

You know what I'm going to do? Potty videos. No, that's a waste of bandwith. I'm just going to note the direction of flow for every toilet I encounter.

Urinals will prove to be challenging.
 
Sac Arrow said:
But I -think- the Eotvos effect is considered to be separate from Coriolis. Coriolis contemplated lateral acceleration/force due to north-south movement, whereas Eotvos contemplated the centripetal component.
...
I don't take issue with the fact that whatever rotational force is there is fairly insignificant. My argument is more with semantics, as to whether it is actually due to the Coriolis effect.
Click to expand...

Ahh, yes OK I understand the question now... As a short answer, there is one "phenomenon" related to velocity that produces both "Coriolis effects" (pushing things left or right) and "Eotvos effects" (pushing things up or down). They are both facets of the same thing. Two components of the same force vector.

Mathematically, the fictitious forces on a moving object are:
[something that goes like omega x (omega x R)] + [something that goes like (omega x v)]

The first bit points outward, and is commonly called the Centrifugal Force. You don't have to be moving to feel this one. It's a vector that points outwards (up towards the sky).

The second bit, for which you have to be moving and which I've been (perhaps confusingly) calling the Coriolis Force, is a vector from a cross-product that can point in a combination of "sideways" and "vertically" depending on your latitude.
If you move north-south, the cross-product is always "Coriolis-style", and goes from zero at the equator to maximum at the poles.
If you move east-west, the cross-product is always maximum, but goes from 100% "Eotvos-style" (that is, vertical) at the equator to 100% "Coriolis-style" (that is, sideways) at the poles.
This is why people just say "The Coriolis effect gets more pronounced as you get closer to the poles" no matter whether you're moving north/south or east/west, and this is true.

Meanwhile, the Eotvos part of the whole thing (the vertical piece of the second equation) gets lumped in or mixed in together with the Centrifugal Force (the first equation), which is also an outward force. Both kinds of outward/inward forces can make something "seem" lighter or heavier on a scale. Both are more extreme at the Equator.

The naming of everything is confusing. Probably for historical reasons. (Does "Coriolis" refer to just the sideways bit, parallel to Earth's surface? Or the whole vector, which can partly point into the sky? I've seen it used both ways.) But I'd say they're both parts of the same happy little vector phenomenon. Love 'em vectors! :)
 
Sac Arrow said:
You know what I'm going to do? Potty videos. No, that's a waste of bandwith. I'm just going to note the direction of flow for every toilet I encounter.

Urinals will prove to be challenging.
Click to expand...
No. Explaining your fascination with the urinal's flushing to the other guys in the can will be challenging.
 
Sac Arrow said:
Let's say you have a non-equatorial river flowing due south in the northern hemisphere.

Which side of the river will be higher than the other?

Why?
Click to expand...

Doesn’t it depend on the position of the moon?
 
Time for a whole bunch of peelots to go read a high school physics book. ;)
 
So which river is this, that has a perfectly smooth bed, no undulations, and the water doesn't slosh and loses all momentum once it turns south?
 
EdFred said:
So which river is this, that has a perfectly smooth bed, no undulations, and the water doesn't slosh and loses all momentum once it turns south?
Click to expand...

You may be on to something. Barring elevations, is it possible for a river to flow north, or south below the equator?
 
bflynn said:
The Coriolis Effect acts on the water of the river. The strongest erosion will be on the right (west) side of the river because the effect slightly enhances water velocity. Albert Einstein was not the first to observe this, but he did write a paper on the topic.
Click to expand...

Not to diminish that you gave the first correct answer. A couple of folks did. It goes to show the POA is a great resource for these kinds of questions.
 
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