Wednesday, February 10, 2010

Topography and Waterpower

I spent some time in the Tyngsboro Boy Scouts growing up, and one of the things they taught us was orienteering - figuring out where you are and how to get where you're going with a compass, and a topographical map - a carefully scaled map with detailed geographical features drawn on it, including elevation contour lines.  I'm a visual learner so I've always liked maps, and along with first aid and riflery, those were what I was best at.  I was probably the worst knot-tier and swimmer in our troop, because I have very little hand-eye coordination or athleticism, and I'm left-handed, but that's ok...I'm getting off topic again.

Well, thanks to the wonders of the modern high-capacity internet tubes and the fact that works of the United States Government are in the public domain, you are now able to download, for free, all sorts of USGS (United States Geological Survey) maps - and I can repost them.  They're in that crazy metric system, but many are one centimeter = 25 meters, or in real measurements, 4/10 of an inch is 82 feet.  So that's what, one inch = 200 feet?  The contour lines are on the three-meter scale, or 9.8 feet.  Every fifth line is darker than the rest, and certain elevations of potential interest are written outright.

You can get the maps here (use the Map Locator button on the left), or you can get the Lowell one directly here.

So, what is the highest point in Lowell?  The lowest?  If sea levels rise as predicted this century, do we stand to own oceanfront property?

Here is the Pawtucket Dam - above 27m (you can see it's one elevation line below the 30m mark) So, the water level is a little under 90 feet above sea level at this point.  Note the falls markers in underneath the University Ave bridge.  The dam itself is about 3m high, then the three markers bring us to the level of the lower river - less than 18m, or around 60 feet.  The 30+ foot drop in elevation here is why we have a city of Lowell at all.

Here we see the end of the Concord River, which is the end of the canal system.  At the end of the Hunt's Falls, the river is now below 15 meters, or 49 feet.

You will also see the reservoir on top of Christian hill is at 71.5m (235ft), and the water tower behind that is 94m(295ft).  This must be the highest point in Lowell.

Fort Hill and Belvidere Hill are 275 and 235 feet respectively.  This map is from the '80s - the old Locks and Canals reservoir is still there.

And Downtown, we see the single drop at Swamp Locks and the double drop at Lower Locks bringing us from 27 meters to 18.  The same as the river.  The third set of locks in Lowell, the Guard Locks up behind the Francis Gate, are just to keep the river, in the event the river level is above 27m, from raising the level of the canal system and flooding the city - hence the name.  The Francis Gate is more sturdy than the Guard Locks and serves to protect the Guard Locks from buckling and failing*.  You can see in the first image that the ground rises very quickly around Francis Gate, trapping floodwaters in a basin, as we saw in the 2006 flood.

*Fun fact:  Lowell locks (most locks anywhere?) are always chevron-shaped, with the point facing upstream.  This is so that the pressure on the high side doesn't force them open.  The Francis Gate is an immobile and extremely heavy piece of wood (or metal as they brace against the gatehouse today instead) so it can withstand the pressure of even higher water levels.

Math geekitude and flooding after the jump...





So, after Lowell, we are below 50 feet above sea level, so what happens next?  The Great Stone Dam in Lawrence drops the river from 15m to 9m.  Before the Lawrence canals empty back into the Merrimack, we are now less than 6m above sea level - a mere 20 feet.  Lawrence has the same 9m, or about 30+ foot drop in elevation as Lowell, hence Lawrence delivered the same amount of power to its mills.  The formula for potential hydropower is

Energy = Flow * Gravity * Head (height).

Well, we know gravity is 9.8m/s^2, and the head is 9 m.  The flow of the Merrimack at Lowell (per http://umlweb.uml.edu/Tsongas/Curriculum_Materials/Curriculum_Packets/PTOP.pdf) is about 100 liters per second, or cubic meters per second, which has a mass of 100,000kg:

Don't worry, I had a lot of help with this formula, it's been a while since I've taken a physics class:

100,000kg/s * 9.8m/s^2 * 9m = 8,820,000J/s = 8,820,000W = 8.8mW = 11,800 horsepower.

This number checks out with the 13,000 horsepower given in the above ULowell link (rounding error I hope!).

Boott Hydro (http://www.enel.it/northamerica/Boott.asp) reports a head of 11m(37ft), and a flow of 227 cubic meters per second (8000 cfs).  That works out to 24,970,000W.  Now, a good turbine is 90% efficient or so, so realistically, we are expecting 22.4MW.  They say they can provide 24MW.  Not a bad estimate!

Why the difference between the UML estimates and Boott's?  I'm assuming the UML estimates date to before Lowell was built (the exercise is on placing a city).  The Pawtucket Dam raised the river level a decent amount (still within reason of the 3m contour scale of the map), and other upstream dams evened out the flow.  Too much water, even today, goes over the top of the dam and can't be used for energy - the levels and flow of the canals are kept fairly steady most of the time.

This exercise that showed me how rusty I am at basic physics shows how much you should appreciate the work of James B. Francis, who was the chief engineer of the canal system for decades.

Floods...

The entire Clay Pit Brook neighborhood is between 27 and 30m.  That's less than 10 feet above the river on a good day.  If the river is high for any reason, be it flooding, or Boott trying to get some extra feet of head (I'm not touching that I don't know enough details), it's not unlikely it'll flood.

How high is the Merrimack at any given time?  The National Weather Service keeps track, and the marker is under the Hunt's Falls Bridge.  We established that's at about 50 feet elevation.  So, you can check this link to see where we are.  Currently, about 44 feet, so 50 feet is within that 3m contour line estimate, or maybe the river is a little low right now, it is winter.

How bad have the floods been? 58 feet for 2006 and 2007.  68 feet for 1936.  So, we're talking 4 meters to 7 meters over the current level.  That's more than one to more than two contour lines above normal.  Note how much of downtown Lowell is under two contour lines above the canals.  Since the water only can enter downtown by backing up the Concord River when the gate is down, compare that to how much of downtown is less than two contour lines above the elevation of the Concord.  It's a lot less.  Again, thank you James B. Francis for that gate!

And to finish up with the River gauges, here is Lawrence.   Perhaps the reason the river is so much lower than the topo maps suggest is because it's below the dam and very little is spilling over?  I don't know.  Either way, it's not too far off.  And more interestingly, here is Haverhill.  If you've ever wondered why Haverhill has a sea wall, here is your answer.  The Merrimack becomes an estuary after leaving Lawrence, meaning that its elevation is so close to sea level that there are ocean tides.  Apparently under current conditions, about four and a half feet.  Note that the Merrimack cuts a pretty deep channel through the entire valley.  There are many elevations in Haverhill that are as high as much of Lowell.  If you've ever been to New York, the Hudson River is an estuary three hours inland, all the way past Albany.  The bluffs around there rising into the mountains are incredible.

So - in closing - this was a much longer, more detailed post than I had intended - even a catastophic two meter sea-level rise wouldn't do much to the Lowell area at all.  Haverhill might get a little wet.

2 comments:

  1. Great analysis of Lowell's topography. I always thought the water tower on Wedge Street in the Highlands was either second or third in elevation in Lowell. I'll have to check that out.

    As for orienteering, it was one of my favorite activities, too, but I fear it will be a disappearing skill now that everyone uses GPS for navigation

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  2. Thanks - the map shows the water tower, and it looks to be at about 57 meters.

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