If Lake Ontario were suddenly emptied, how long would it take Niagara Falls to fill it back up?
(I actually calculated an answer to this question and I’m wondering how far off I am. My answer is rather longer than I expected. Also, if you’d like to be competitive, time yourself to see how long it takes you to come up with an answer.)
approximately 820 days?
Average flow rate of Niagara Falls: 1833 m[sup]3[/sup]/s.
Volume of Lake Ontario: 1640 km[sup]3[/sup] = 1.640 x 10[sup]12[/sup] m[sup]3[/sup].
Time to fill = 1.640 x 10[sup]12[/sup] m[sup]3[/sup] / 1833 m[sup]3[/sup]/s = 8.94 x 10[sup]8[/sup] s = 28.4 years.
Show your work.
Is Niagara Falls the only source of Lake Ontario’s water supply?
If you use the average flow you will get an estimated time, as Sunspace calculated. However his answer holds only if you stop up the St. Lawrence river and do not allow any outflow, and ignore evaporation.
If you wanted a more precise answer, you should use historical data or synthetic data which has been calibrated. Then the answer will be “it depends upon when you are refilling”.
You’d also need to account for outflows and evaporation.
It is the primary source. Its drainage area is so large that the runoff from the area around Lake Ontario could probably be considered trivial.
Interestingly, this article in the Canadian Encyclopedia mentions that the average flow in the Niagara River at Queenston is 5760 m[sup]3[/sup]/s. If true, this implies that the hydroelectric generating stations around Niagara Falls take more than half of the Niagara River’s water!
Of course not. But I wonder how all the other sources compare in total volume. We could calculate that by finding the average yearly runoff from the Lake Ontario watershed (minus the Niagara River).
Wiki lists several other rivers, of which the Genessee is much the largest. But with an average flow around 125 m[sup]3[/sup]/s, when compared to what Sunspace cites for the Niagara River it is pretty close to trivial (as NinetyWt suggests).
Principal rivers flowing into Lake Ontario, New York side:
This gives us 18,672 cu ft/sec average flow for New York rivers other than the Niagara.
If the wiggly blue lines on physical maps of Ontario do in fact represent rivers, Natural Resources Canada is doing a remarkably good job of keeping their identities secret. Two river systems I know are there are the Trent and the Caztaraqui – the latter’s mouth is at Kingston, where the St. Lawrence takes up Lake Ontario’s outflow, but my assumption is that if Lake Ontario were an empty depression, it would flow ‘upstream’ down the slope of the former lake bottom to aid in refilling the lake before any water went down the St. Lawrence.
There are no figures giving rate of flow for Ontario Rivers. In view of the fact that the land is less rugged and the Lake Ontario watershed somewhat less extensive than New York’s, make an arbitrary guess of 2/3 of News York’s flow, or 12,000 cu ft/sec.
The total discharge into Lake Ontario from state and province is therefore on the order of 30,000 cu ft/sec. Taking 1833 cu meters/sec and converting to cubic feet, we get 64,770. So the Niagara River contributes slightly over two-thirds of the total inflow into Lake Ontario, but the other streams discharging into it appear to contribute about another scant third. Granted, this is making some arbitrary assumptions, but they are ones I believe are justified from observation of flows and terrain.
In addition to the Trent and the Cataraqui, a few that come to mind include the Humber and the Don (both in Toronto), the Moira (in Belleville), the Jordan (Jordan), the Rouge (Pickering), the Ganaraska (Port Hope) and a number of others whose names escape me right now. I cannot find any information on flow rates, but if anybody else would like to try, there are some names to search on.
Mind, these are pretty small compared to the Niagara River, so I don’t think they would contribute much.
But, as Sunspace has noted, that’s the flow over the falls, and omits the flow that’s bypassed for power generation. The actual flow of the Niagara River is more than 3 times 64,770 cfs.
[Note: In my post above, it seems I overlooked the Oswego River.]
There’s also some coming through the Welland Canal, although I have no idea how much.
Don’t forget that a lake’s drainage area includes the lake itself. There’s probably a fair amount of rain that falls directly into the lake without bothering with any river.
Yep. They would take even more, except that the Falls generate (pun intended) too much tourism to shut them down to too great an extent. But the Niagara River could be exploited more heavily if we wanted to do so.
Still, what you see is a fraction of what the Falls used to look like. However, the experience from 1969, when engineers diverted the flow away from the American side to study whether it needed shoring, shows vividly why they won’t take any more.
Taking the full Niagara flow of 5760 m[sup]3[/sup]/s mentioned earlier, and repeating the earlier calculation:
Volume of Lake Ontario: 1640 km[sup]3[/sup] = 1.640 x 10[sup]12[/sup] m[sup]3[/sup].
Time to fill = 1.640 x 10[sup]12[/sup] m[sup]3[/sup] / (5760 m[sup]3[/sup]/s) = 2.85 x 10[sup]8[/sup] s = 9.02 years.
If we take Polycarp’s figure of 30 000 ft[sup]3[/sup]/sec for non-Niagara drainage we get:
(30 000 ft[sup]3[/sup]/s) * 0.028 (m[sup]3[/sup]/s) / 1 (cu ft/sec) = 840 m[sup]3[/sup]/s (only!).
Add the full Niagara flow of 5760 m[sup]3[/sup]/s, and we have a total of 6600 m[sup]3[/sup]/s.
Repeating the earlier calculation:
Volume of Lake Ontario: 1640 km[sup]3[/sup] = 1.640 x 10[sup]12[/sup] m[sup]3[/sup].
Time to fill = 1.640 x 10[sup]12[/sup] m[sup]3[/sup] / (6600 m[sup]3[/sup]/s) = 2.48 x 10[sup]8[/sup] s = 7.87 years.
My apologies for taking the unimpeded flow of the Niagara for the total flow. With that correction, and presuming my assumptions to be accurate, the Niagara River provides 87% of the surface flow into Lake Ontario, with the other rivers flowing into it providing 13%. I tried to work a calculation for the equivalent of inflow from direct rainfall on the lake, but failed.
Relevant facts: The area around the lake averages 32-64 inches annual precipitation. The lake has a surface area of 7,340 square miles. The results need to be in cubic meters/second to match the inflow rates. My figures suggested that annual precipitation on the lake surface is over 90% of the total inflow from the whole watershed, which suggests to me I applied erroneous figures. Anyone want to take a shot at it?
Does most precipitation that falls on land make it into the stream system? Or could it be that a lot of it evaporates (and a tiny portion otherwise used) before it enters a stream?
OP here – this is basically the same answer I came up with (I just said “about 30 years”). I made the following simplifying assumptions:
As pointed out by other posters, these assumptions are not realistic. But hey, if I can empty Lake Ontario with a snap of my fingers, I can sure take care of those minor quibbles! 
I surprise $160 water bill has me doing this math on a much smaller scale today. 