# How long can a river physically be on a planet?

How long can a river be? Are there any physical limits on its length, coming from the necessary altitude drop, the triple point of water, or other factors? You can alter whatever parameters you find necessary for the planet that contains this river. Any pressure, continent distributions, densities, diameters etc; are allowed but the river must be made of liquid water and be on the planet's surface.

• How big is the planet? The bigger the planet, the longer it can be... – Aify Jan 27 '16 at 6:44
• Are you familiar with River world by Jose Farmer? – King-Ink Jan 27 '16 at 7:45
• Define river. For example, the Mississippi is a river, but a lot of its length comes from feeder rivers. The Mississippi basin is a lot bigger than the Mississippi river. Do you only care about rivers that feed into a lake or sea? Does a river need to flow? Would a channel round the planet's equator, full of water, count? This could be a couple of kilometers across, but there are rivers getting to that kind of width, especially in delta areas. Do underground water flows count? What about underwater flows? Lots of options here! – Matthew Jan 27 '16 at 7:59
• You need to constrain the width of the river to something reasonable. Otherwise it can be arbitrarily slow, arbitrarily narrow and arbitrarily deep so that it won't evaporate before covering the entire planet in a space-filling curve. However, you have implied a limit on the size of the planet; that it must be able to support an atmosphere where water can evaporate and condense to keep the river topped up. – sh1 Jan 27 '16 at 8:17
• The material that makes up the surface of the planet is also relevant, as is the weather (or the means by which water enters the system -- is it a constant rate? Does it vary by volume at all? etc). Erosion could cause forks in the river, which may lead to water changing the overall direction of the flow, e.g. if there is a lot of zig zagging, it may erode away the mountains separating the zig from the zag over time. – Casey Kuball Jan 28 '16 at 21:26

Imagine a square kilometre. The north-west corner is 100 m higher than the south-seas corner. I'll think of the river as a zero-width line to simplify calculations, you'd have to make allowances for that in the extreme cases.

• A river would certainly flow if it went straight from NW to SE. The length is $\sqrt{2}$ km and the gradient is about 70 m per km.
• If the area was cut into serpentines, the river could zig-zag back and forth. Ten serpentines give a length of about 11 km and a gradient of about 9 m per km. Twenty serpentines give a length of about 21 km and a gradient of about 5 m per km. 100 serpentines would give a river length of about 100 km and a gradient of 1 m per km.

Streams in low plains regions can have a gradient of less than 1 m per km. So if the area did consist of alternating strips of very hard rock and soft soil, with some judicious digging there could be 100 km of creek (perhaps 5 m wide) on one square km.

To get a halfway realistic geography, it would be less than this constructed example. The gradient is probably the main limitation. If the springs are at an altitude of 5 km, you can easily get 5,000 km of river as it meanders down to sea level.

• I started with a solution like that, but stopped when I realised that if the flow is too slow then it'll evaporate before it gets to the end. I couldn't be bothered with the research to find a viable limit. – sh1 Jan 27 '16 at 7:35
• The slope of 1:1000 seems to be slightly surpassed by Earth rivers: the Amazon and the Nile are each around 7,000 km long, but the Amazon starts on a 5.5 km tall mountain and the source of the Nile is no higher than around 2 km. A ratio of 1:10,000 or higher may be possible, especially on a planet with very high gravity. – 2012rcampion Jan 27 '16 at 8:28
• Minneapolis to New Orleans is under 1000 ft vertical and over 1000 miles as the crow flies. The Missisippi is notoriously far from straight. So at least 1:6000 and I'd easily believe 1:10000 – nigel222 Jan 27 '16 at 9:07
• I'm failing to work out in my head if there is any way that a topologically circular river going all the way around a planet could be made to flow in one preferred direction by tidal drag, coriolis effect and prevailing climate and winds. If it could then it's "length" might be said to be infinite. Would obviously have to be a rather dry planet or a heavily engineered one. – nigel222 Jan 27 '16 at 9:18

## How far from the source to the sea?

There are certain constraints to the length of the river.

Meanders change their shape perpetually. The current state of the meanders is categorized by the numeric ratio between the length of the river bed (the water course length), and the length of the river in air-distance measure (the distance between its end points). This ratio is called: "The meander-ratio". The most common meander-ratio is approximately 3:2. - [source]

It goes on to say that the river Jordan has a ratio of 2:1 which is unusually high, so you're looking at an upper limit of twice the air distance from source to destination as the crow flies.

Of course this is how long a river would be rather than how long it could be, but given a million years or so a river will take shortcuts through hills and mountains that might be in their way, no matter how much the hard rock and the soft ground try to make them go the long way round.

The only limit is the size of the planet itself

If the river is exactly situated at the equator, if the altitude at the equator is constant and if the Coriolis forces (due to planet rotation) are sufficient enough then an infinite unidirectional stream is possible.

Considering the 3 conditions are fulfilled, your river may be as large as the planet's circumference.

• Should make that half the planet's circumference, rather than diameter, since rivers generally flow on the surface of planets. Even if they go underground, they don't typically go through the center of the planet. (Unless it's Naboo - which still makes no sense to me...) – Darrel Hoffman Jan 27 '16 at 19:36
• Of course you were right. I edited, thanks for pointing it out. – Kii Jan 27 '16 at 19:52