Do lakes slope?

I’m on holiday in the Lake District and it’s raining. All that water falls down out of the sky and ends up in streams and becks and ghylls and rivers and so on. These then go into the tarns and lakes. The water enters at the edges, not in the middle (apart from rain falling on the lake’s surface). It has an outflow too.

So, is the surface of the lake sloping away from the inlets, towards the outlet?

The rate of incoming flow to a lake from rain will be insufficient to cause it to slope.

However if you go over the connel bridge and look at the Falls of Lora as the water leaves Loch Etive then you really can see the water sloping – the water at one side of the big rock is about 1m higher than the downstream side. Very impressive to see!

Water is flat, it’ll overspill at the lowest point on the perimeter.

It won’t be flat, it will be curved like the earth

It takes time to move though so surely if it’s coming in at one end and going out at the other it will be very slightly higher at the ‘in’ end than the ‘out’ end? Unless these two flows are exactly equal and an equilibrium has already been reached? If there’s no out but ins all around, like in a lake, then would it be slightly higher at the sides and not quite as high in the middle? Just thinking to myself, hence the question marks.

Also, on a sufficiently large body of water (actually on all, but i doubt it will be measurable on small ones) tides will make it higher at one end than the other.

And, again more noticeable on big ones, the curvature of the earth will mean it’s not flat anyway.

I wait to be corrected by people who actually know about this stuff

[Edit] the other Andy thinks I’m right about at least one of these things, I’ll take that

You have to take into account the gravitational pull of the moon also, as that can cause slight bulges.

Lakes must slope – how else can you water ski?

There’s also friction between the water molecules which will lead to sloping.

True level.

Strong wind might cause them to slope. For the flow of water to cause them to slope to a measurable degree, they would basically have to be a river with a very noticeable current.

Wouldn’t they slope for a while if there was a rapid change in flow?

So, is the surface of the lake sloping away from the inlets, towards the outlet?

If more water enters at the edges then it’ll be bowl-shaped and lower in the centre, stoopid 🙂

Are you factoring in Glacial isostatic adjustment ??

Depending on the strength and direction of the wind the water can and does pile up on one side of the lake compared with another.  Llyn Tegid in Eryri is prone to this during gales as length of the lake down the valley aligns with the southwesterly winds and water can pile up on the NE shore (we’re usually talking centimeters in difference here though) – this wind driven surge is different from waves.
Very large lakes (Huron/Superior etc) perhaps even Loch Ness and Neagh may even have differences in elevatation caused by differences in air pressure at different ends of the lake – especially in fast changing weather conditions, although it may be hard to distinguish the pressure surge component from the wind driven surge component.

It won’t be flat, it will be curved like the earth

Burn the witch!!

what happens if you put a treadmill under the streams running into the lake, with the speed of the upwards treadmill belt being equal to the water speed trying to go down hill? You could create some very sloping lakes that way!

The incoming water has an incompressible volume so it surely must contribute to the ‘size’ of the lake at that point before it flows away, spreading outwards.

Ness and Neagh aren’t big enough for storm surge/low pressure weather phenomena

The Great Lakes however do experience them but it is highly wind direction dependent as with all surge events. You also  need “fetch” for surge

If in a very mountainous region there may be a very slight difference in the gravity fields near the shores due to the elevated position of the rocks/mountains – this would “pull” water towards the mountainous shores of the lake and away from the centre of the lake – but in reality the effect would be tiny in most lakes.
The effect is important though in sea level rise projections  – Greenland’s gravitational mass will reduce as the enormous, heavy ice sheet on top of it continues to melt in coming years and as its mass reduces it will “pull” less sea towards Greenland allowing it to spread out into the Atlantic.  This changing gravitational sea level component will be (one reason) why sea level will increase more in some parts of the north Atlantic coastal areas than in others over future years.

You have to take into account the gravitational pull of the moon also, as that can cause slight bulges.

There’s a gravity hole in the Indian Ocean. The effect of gravity is weaker there than the rest of the planet and the sea level surrounding Southern India and Sri Lanka is on average 100 ft lower than the rest of the ocean.

Does the Earth’s rotation have an effect too?

What gradient are we classing as a slope? Rivers slope, Lakes? I’d say not, although there could be a level difference…..

I’d say that in order for something to have a slope it must be possible for something to move predictably on it by the force of gravity alone.

A lake will have a very moderate slope, ignoring weather conditions (assuming there’s inflow and outflow). A river has a bit more of a slope. If they didn’t slope, the flow would stop due to friction.

The slopes are modest but easily measurable in the case of rivers. The OS map shows the Ribble crossing a couple of contour lines local to me (without there being any rapids or weir). Lake flow is very very much slower and therefore the required slope is much much smaller and probably dwarfed by wind effects usually.

Since everyone is into stand up paddle boarding now, can’t one of you go check out the flatness of a local lake with a spirit level?

It will be flat, but it will also be curved as it sits on a planet that is curved and gravity will be pulling down on it equally across the whole surface. So at each point you are standing (or floating), you will be at the highest point of the curve that you are looking at as the planet curves away from you in all directions.

Lakes fed by inflowing streams/rivers will have a slope, it will depend on the delta between inflow and outflow, shape of the lake, prevailing climatic conditions, etc. It won’t be significant.

Any direction I attempt to swim in will be uphill. This seems to be a very localised phenomenon.

Yes, otherwise you would have no flow.

But the pressure drop along the length of the lake is tiny because the velocity is so low (tens m3/s spread over tens of thousands of m2)

If you could be bothered to calculate it then I suspect it’s of the same sort of order of magnitude as the surface tension.

Yes, otherwise you would have no flow.

If there is a discharge point you will have flow, it doesn’t need to slope to have flow.

Is the water in a bath sloping when it discharges out of the overflow? Water in, and water out = flow.

Is the water in a bath sloping when it discharges out of the overflow?

Yes, it’s a bit different a bath as the fill and overflow tend to be in the same place so that complicates things.

Water in, and water out = flow.

Flow is an attempt to balance potential energy, as there is always friction in a system that will leave a surface gradient. You can see it on hydrographs at the opposite end of lakes, the outlet doesn’t start responding immediately the incoming flow increases and the outflow can remain higher after the incoming surge has finished. Water is incompressible so that has to be through a surface gradient.

Does the Earth’s rotation have an effect too?

you’d get a real tank slapper if the earth suddenly stopped

I know quite a few of the responses are from hydrologists, hydraulicists and engineers, including atleast one colleague.

I also know i know enough to really show my ignorance.

So i am keeping my mouth shut.

I suspect i know the answer and that it is above.

But what i will say in oder to keep standards high.

OP you are incorrect, actually very little of the rain falling in he lake district ends up in lakes.

I’m not going to argue with anyone as lots are correct in certain ways. I have some knowledge, from an engineering design point of view, but really it’s all about how technical you want to get. I’m certainly not going to get technical about it, but as I said earlier, what actually constitutes a slope and what do we say is flat. From an engineering POV this may well be different to other scientific types.

I don’t consider the curvature of the earth to be a slope….

Oh and Hi Josh!

If there is a discharge point you will have flow, it doesn’t need to slope to have flow.

Yes it does. [edit: excluding external forces like a difference in atmospheric pressure)

Is the water in a bath sloping when it discharges out of the overflow? Water in, and water out = flow.

In a liquid filled pipe that would be correct, and you would have a pressure drop along the length of the pipe.

In a  bath (or a lake) that pressure drop means there is more pressure at the in end than the out end (it’s after all, just a pipe with only 3 sides).  If you have more pressure then you have more static head, if you have static head you have height, if you have a difference in height you have a slope!

Because everything is better with pictures.

Top – small pipe, big pressure difference along it

Middle – big pipe, small pressure difference

Bottom big pipe with the top removed.

P1 and P2 have to be moved for the last one because otherwise you’d be measuring 0 differential pressure because the slope of the surface is in effect a line of equal pressure (an isobar).

Love @gwaelod’s reply 🙂

There has been some efforts to measure the ‘slope’ and tides on Loch Ness, for example: https://journals.ametsoc.org/view/journals/atot/33/6/jtech-d-15-0162_1.xml and https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2011JC007411

Ha was about to post the Loch Ness tides – note it’s not the direct gravitational force from the moon, but the secondary effect of the ocean tides around the coast.

Love stw thread basically about reference frames. I think it’s why some people find physics ‘hard’ because … what is ‘level’ and what are you counting a ‘slope’ from? You have to place the question in terms of gravity, pressure difference, and friction. So you are starting in the reference frame of a gravitational equipotential – a surface of equal gravity. This is affected by the mass of the solid Earth, or of the water body or adjacent water / ice. And then extra flow in affects the mass in the lake (or river or sea or ocean) with the laws of physics redistributes, with all the other forces from air/wind, surface friction, bottom friction, temperature and salinity affecting density, gives you a new ‘level’. If more mass enters ‘upstream’ than can get through the lake and exit ‘downstream’ the slope will increase for a while and at the same time the whole lake level will rise, but usually by tiny amounts because the lakes are so big. I don’t know for the Lake District but some reservoirs can delay the peak river level downstream after a big rainfall event by 2 days.

What about the floaters from the primary effluent discharges? Does that give you a lumpy, smelly slope?

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