I don’t think that necessarily follows. Imagine a barrel of water with an inflow pipe 1 foot below the surface, and an outflow pipe 2 feet below the surface. Water can flow into and out of the barrel while the water surface remains horizontal.
The great lakes experience fluctuations in level (which manifest in a similar way to tides), caused by wind blowing the water around into heaps. I imagine this might confound any such measurements.
The Great Lakes are just very wide rivers, topologically speaking. They are not barrels.
Not sure that’s strictly correct; thought experiment:
If you have a barrel with just an outflow pipe on the right, it will drain, but if it’s draining from one side, the water level will fall at the right first - the flow of water will try to level that out, but it does theoretically create a gradient.
If you have a barrel with an inflow on the left, water will pile up a bit on that side until it levels out.
If you combine those two things, you have flowing water with a gradient. It might be immeasurably small in a vessel the size of a barrel, or might be swamped by the noise of turbulence, etc.
You may be right, but I think it’s a question of scale rather than topology. If you have a very large & deep reservoir of water with only a relatively small inflow and outflow, the surface can be horizontal, as in the barrel analogy.
Imagine a lake created by a dam, for example.
Can it? That seems to contradict what I’ve learned from this thread.
The barrel example has the inflow and outflow below the surface, while the rivers filling and draining the Great Lakes are on the surface. I don’t know if that’s relevant.
Not a good example since the Thames at that point is tidal and quite fast flowing in both directions.
The idea that ice on a slow-flowing river might have an incline is interesting though. My WAG is that, since it does not freeze all at once, the surface of the ice would average as a slope, but with lots of variation.
The usual range of the Thames Tideway at Tower Pier is between -2.88m and 4.25m. It has been between these levels for 90% of the time since monitoring began.
The typical recent level of the Thames Tideway at Tower Pier over the past 12 months has been between -3.00m and 4.42m. It has been between these levels for at least 150 days in the past year.
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The highest level ever recorded at the Thames Tideway at Tower Pier is 4.81m, reached on Thursday 1st March 1990 at 4:00am.
All heights are relative to sea level.
Another way to conceptualise this: if it were true that the surface of a river were flat (wrt height above sea level), then in those places where a river gets shallower as you go downstream (i.e not the general case, but in places where it broadens out, or where underlying bedrock prevents the channel being cut any deeper), water would be flowing uphill.
Just as it does in an estuary when the tide comes in
During which time the upper surface of the water is not flat.
I think this is fairly accurate, but irrelevant to the question of non-horizontal surfaces. This example has no net flow in the horizontal dimension along which we question the slope. Any slope would arise from the resistance encountered by horizontal flow only.
(Snip overly complicated answer) look up the Mississippi river and the Erie Canal for real world cases. Mississippi averages out to 0.01% slope between St Louis and New Orleans, and was so useful because that was flat enough for barges going downriver and powered boats going up. They cut canals to replace “waterfalls, rapids, and other turbulent-water situations” with smoothly sloped sections. Also dredging and dikes to deepen the river where there might have been rapids before. Don’t even need any locks for large elevation changes over those 1000 miles. So that’s your smooth water surface with non-zero slope.
The Erie Canal is important because man-made fixes lots of variables. Dug to a 40 foot x 4 foot cross section the whole way. No bumps on the bottom, sudden height changes, or rocky bits to cause turbulence. The locks are just there for large height changes so the long stretches can be smooth drops.
From a physics perspective, changes in the shape & composition of the channel are what cause the turbulence etc. From conservation of energy & gravity type equations, an ideal water flow would be locally flat (that equipotential surface), and globally a smooth slope (the equations basically require smooth solutions if there aren’t sudden discontinuities upin the system). Right at inlets, outflows, elevation changes and the like are areas of change where things aren’t in static equilibrium so you need fancier calculations, but they have to fade to equilibrium as you get away from those points.
Lots of other stuff I could say but it would just muddy the waters. I’ll just mention that seeing floods on the Mississippi is educational. Flooding events are locally flat & smooth, but the height change slowly travels down the length of the river, and is still smooth even when the water is rising. Oh, and yes high water in the main channel will back up into & raise the water level of feeder rivers, creeks, back yards, etc
That’s fantastic real-world information, thank you Chopstick.
If I’ve understood you correctly the Lower Mississippi is approximately 1,000 miles long with an average slope of 0.01%, so although the gradient is imperceptible the water level at Saint Louis is 160 metres higher than at New Orleans.
Maybe not a good example in the sense that there are confounding factors. But it was precisely the question of how tides propagate upriver (which I still don’t fully understand) that got me wondering about my assumption that the tidal section of the river is all at sea level.
First off, “sea level” is an average measurement taken over a number of years to determine a baseline. You will no doubt have seen warnings of rising sea levels due to climate change.
The surface of the water in an estuary can be higher or lower than that average as the tides rise and fall attracted by the moon’s (and to a lesser extent the sun’s) gravity.
As the tide rises, it pushes water into the estuary, causing the level to rise and the direction of flow to be reversed. The actual mechanics are complicated.
This is the bit I am interested in. I am not convinced that the direction of flow is reversed throughout the length of the Tideway as far as Teddington Weir. In my experience with the River Liffey in Dublin, the direction of flow continues to be in the downstream direction (albeit slower) even as the level is rising due to the incoming tide. The level rise is due to the river “backing up” rather than the channel being filled with seawater.
The surface of the water will remain almost horizontal. For small flow like that, the angle of the surface will be almost directly proportional to the length of the pipe, and amount of flow. So very horizontal, but not horizontal.
If you have a very large & deep reservoir, the surface can form a portion of an obloid sphere, modified by the rotation of the earth, the sun, the moon, air pressure and the effect of local gravity. But the basic equation of drift is that flow is proportional to surface angle.
I can’t find a good reference, but here’s an old difficult reference: as I understand it, maybe 40 cm difference between the ‘equal’ value of lake elevation, and the ‘local’ value of lake elevation.
You did this on purpose, right?
Indeed - because the incoming tide is a descending surface gradient