Lockage Water Used

[enigma]

Sometime ago there was a thread about the amount of water used by boats of different sizes/weights when travelling through locks. As usual there were several different ideas.

 

The answer is in this article copied from "Bradshaw's Canals and Navigable Rivers."

 

Mr G R Jebb in a paper on the "Maintenance of Canals" read before the Society of Arts Conference on Canals, 1888, gives the following information on a point connected with the consumption of lockage water.

"A boat locking down from the higher to lower level requires a lock full of water minus the amount it displaces; a boat locking up from a lower level to a higher level requires a lock full of water plus the amount it displaces; thus it will be seen that a loaded boat requires more than an empty one when locking uphill, and that an empty one requires more water than a loaded one when locking down hill."

 

 

A boat locking down from the higher to lower level requires a lock full of water minus the amount it displaces.

A boat locking up from a lower level to a higher level requires a lock full of water plus the amount it displaces.

An empty boat requires more water than a loaded one when locking down hill.

A loaded boat requires less water than an empty one when locking up hill.

Edited November 30, 2015 by enigma

[Machpoint005]

It's still wrong because the amount of water the boat displaces is the same regardless of whether the lock is "full" or "empty".

...unless somebody unloads it while it's in the lock, of course.

[bassplayer]

Sometime ago there was a thread about the amount of water used by boats of different sizes/weights when travelling through locks. As usual there were several different ideas.

 

The answer is in this article copied from "Bradshaw's Canals and Navigable Rivers."

 

Mr G R Jebb in a paper on the "Maintenance of Canals" read before the Society of Arts Conference on Canals, 1888, gives the following information on a point connected with the consumption of lockage water.

"A boat locking down from the higher to lower level requires a lock full of water minus the amount it displaces; a boat locking up from a lower level to a higher level requires a lock full of water plus the amount it displaces; thus it will be seen that a loaded boat requires more than an empty one when locking uphill, and that an empty one requires more water than a loaded one when locking down hill."

 

 

A boat locking down from the higher to lower level requires a lock full of water minus the amount it displaces.

A boat locking up from a lower level to a higher level requires a lock full of water plus the amount it displaces.

An empty boat requires more water than a loaded one when locking down hill.

A loaded boat requires less water than an empty one when locking up hill.

Surely the more the water is displaced (replaced) by a boat in a lock, the less water is required (regardless of whether you are going up or down).

Edited November 30, 2015 by bassplayer

[Colin North]

I think I agree with the OP.

When you enter a lock to go down you are already displacing water. When you leave the lock, the water from the lower level fills the hole you have made in the water.

When you enter a lock to go up you have already displaced the water, you go up and have still displaced the water. As you move out water flows into the lock to fill the hole that your boat is.

This is nit-picking a bit and is much easier to imagine if you think in terms of a boat much larger that ours that more or less completely fills the lock.

[Machpoint005]

Surely the more the water that is displaced (replaced) by a boat in a lock, the less water is required (regardless of whether you are going up or down).

 

No, because it doesn't stop displacing water at any time. The difference between 'full' and 'empty' is constant, and that's what matters. The thing liable to confuse is that an 'empty' lock still has water in it!

[Loafer]

Is it also true that a boat going up a flight of 5 locks uses 5 locks' worth of water, whereas a boat going down only uses ONE?

[Machpoint005]

I think I agree with the OP.

When you enter a lock to go down you are already displacing water. When you leave the lock, the water from the lower level fills the hole you have made in the water.

When you enter a lock to go up you have already displaced the water, you go up and have still displaced the water. As you move out water flows into the lock to fill the hole that your boat is.

This is nit-picking a bit and is much easier to imagine if you think in terms of a boat much larger that ours that more or less completely fills the lock.

 

You still have to push out some of the water in the 'full' lock in order to get into it!

Is it also true that a boat going up a flight of 5 locks uses 5 locks' worth of water, whereas a boat going down only uses ONE?

 

No. it moves one lockful down each lock, so if they are all the same size, one lockful altogether. The direction of travel is immaterial.

[Steilsteven]

Mr Jebb was wrong, the amount of water used is the same regardless, large or small boat, uphill or downhill.

When a boat is at the top of a lock it displaces the same amount as when it's at the bottom of the lock.

 

Keith

[Loafer]

[Iain_S]

Is it also true that a boat going up a flight of 5 locks uses 5 locks' worth of water, whereas a boat going down only uses ONE?

 

It depends.

 

For example,Forth and Clyde locks have no bywashes,and so always fill due to the water from the summit reservoir flowing downhill. Therefore, when locking up, you pull a lockfull from the upper pound to fill the lock you're in, but this is replaced when you empty the next lock before entering. The result is that going up the flight uses one lockfull of water.

Going down, each lock needs emptied,and this runs down to the next lock, where it overflows and continues down the flight. You therefore use one lockfull per lock.

 

In other places, assuming the lock pounds are "on weir",locking down will use a lockfull per lock if the locks are full, and one lockfull per flight if the locks are empty, and the lower lock is started filling before the upper lock is emptied. Locking up, it's one lockfull per flight, whether the locks are full or empty.

 

In practice, it's not as clear cut, as the water takes time to find its level, lock pounds vary in size, locks are usually in some intermediate state between full and empty weir levels vary, etc, etc.

[PaulG]

Going downhill:

When the boat enters the lock it displaces an amount of water equal to it's weight (its displacement). When the lock is emptied, it releases a volume of water equal to the volume of the lock less the boats displacement.

As the boat leaves the lock, and amount of water equal to its displacement is drawn into the lock from the lower level.

So the water "used" (i.e.let down from the upper level to the lower one) is water equal to the volume of the lock, less the boats displacement.

 

Going uphill:

When the boat enters the lock it displaces an amount of water equal to it's weight (its displacement).

To fill the lock requires a volume of water equal to the volume of the lock, less the boats displacement.

When the gate is opened, and the boat exits the lock, a volume of water equal to the boat's displacement flows into the lock from the upper level.

The boat has now "used" a volume of water equal the the volume of the lock chamber.

 

So Mr. Jepp is correct.

A boat going down uses less water than a boat going up.

[bassplayer]

Hmm...so....

 

When a boat enters a lock to go down, it pushes water from the lock back into the top pound. So the upper pound gains some water as a result of the boat entering the lock. When the boat leaves the lock, the hole left behind the boat in the lock is filled with that from the lower pound.

 

So when the boat is going down, the upper pound gained a boats worth of water at the expense of the lower pound.

 

When a boat enters a lock to go up, it pushes water from the lock back into the lower pound. So the lower pound gains some water as a result of the boat entering the lock. When the boat leaves the lock, the hole left behind the boat in the lock is filled with that from the upper pound.

 

So when be boat is going up, the lower pound gained a boats worth of water at the expense of the upper pound.

 

So by my dodgy logic, is the answer that overall, water loss is not affected by the displacement of the boat? (so long as boats go up and down).

[Machpoint005]

Mr Jebb was wrong, the amount of water used is the same regardless, large or small boat, uphill or downhill.

When a boat is at the top of a lock it displaces the same amount as when it's at the bottom of the lock.

 

Keith

 

This is the argument I've been trying to explain for years. You are right. We all know that there may be by-washes or weirs on some canals, some locks may hold rather more water than others in the same flight, but in the grand scheme of things, using a lock uses one lockful of water whether you are going up or down. OK, sometimes the lock may be against you, but it all cancels out in the end to the best approximation. The size of the boat (or the complete lack of any boat!) makes absolutely no difference to the amount of water going through the paddles,

>> So by my dodgy logic, is the answer that overall, water loss is not affected by the displacement of the boat? (so long as boats go up and down).

 

Your logic is sound. You are correct.

..for 'boat's worth; read 'lockful'.

A lockful is the difference between the top level pound and the bottom level pound, times the average length and width of the chamber.

[Scholar Gypsy]

It won't surprise some earlier readers to know I agree with Mr Jebb, and with bassplayer.

 

It rather depends on what question you are asking. If the volume of the lock is V and the displacement of the boat is D, then there are four questions:

 

1) How much water does it take to fill an empty lock with no boat in it?: V

2) How much water does it take to fill an empty lock with a boat in it? V

3) If a boat travels from the lower pound (starting with the lock empty) to the upper pound, leaving the lock empty, how much water moves from the upper to the lower pound? V+D

4) If a boat travels from the upper pound (starting with the lock empty) to the lower pound, leaving the lock empty, how much water moves from the upper to the lower pound? V-D

 

A lot of the earlier thread focussed on 1) and 2) - it can be surprising that the answer is the same. Actually I think the important questions are 3) and 4).

 

Another way to think about this is the conservation of energy. It takes energy to lift a boat uphill (weight x height lifted), and this has to come from somewhere (hence V+D). Conversely energy is released when you drop a boat 6 feet (hence V-D).

[Machpoint005]

It won't surprise some earlier readers to know I agree with Mr Jebb, and with bassplayer.

 

It rather depends on what question you are asking. If the volume of the lock is V and the displacement of the boat is D, then there are four questions:

 

1) How much water does it take to fill an empty lock with no boat in it?: V

2) How much water does it take to fill an empty lock with a boat in it? V

3) If a boat travels from the lower pound (starting with the lock empty) to the upper pound, leaving the lock empty, how much water moves from the upper to the lower pound? V+D

4) If a boat travels from the upper pound (starting with the lock empty) to the lower pound, leaving the lock empty, how much water moves from the upper to the lower pound? V-D

 

A lot of the earlier thread focussed on 1) and 2) - it can be surprising that the answer is the same. Actually I think the important questions are 3) and 4).

 

Another way to think about this is the conservation of energy. It takes energy to lift a boat uphill (weight x height lifted), and this has to come from somewhere (hence V+D). Conversely energy is released when you drop a boat 6 feet (hence V-D).

 

Energy is conserved without you even thinking about it.

 

When a body is partially or totally immersed in a fluid, it experiences an upthrust equal to the weight of fluid displaced. Mr Archimedes worked that one out a long time ago.

 

In other words, it doesn't matter whether it's a boat plus water, or just water, it's the same amount of potential energy (for that is what it is) that gets lost.

The energy 'lifting' the boat is exactly the same as the energy lost when the water comes down, whether or not there's a boat along for the ride.

...which is why your (3) and (4) are incorrect. It's the same volume of water, one lockful, regardless.

[Steilsteven]

It won't surprise some earlier readers to know I agree with Mr Jebb, and with bassplayer.

 

It rather depends on what question you are asking. If the volume of the lock is V and the displacement of the boat is D, then there are four questions:

 

1) How much water does it take to fill an empty lock with no boat in it?: V

2) How much water does it take to fill an empty lock with a boat in it? V

3) If a boat travels from the lower pound (starting with the lock empty) to the upper pound, leaving the lock empty, how much water moves from the upper to the lower pound? V+D

4) If a boat travels from the upper pound (starting with the lock empty) to the lower pound, leaving the lock empty, how much water moves from the upper to the lower pound? V-D

 

A lot of the earlier thread focussed on 1) and 2) - it can be surprising that the answer is the same. Actually I think the important questions are 3) and 4).

 

Another way to think about this is the conservation of energy. It takes energy to lift a boat uphill (weight x height lifted), and this has to come from somewhere (hence V+D). Conversely energy is released when you drop a boat 6 feet (hence V-D).

I understand what you're saying but, for it to be right, the boat would need to be sitting on the bottom of a lock totally devoid of water either before going up or coming down.

 

Keith

[Ray T]

When I go boating I'm just glad there is water in any lock I use.

[Machpoint005]

Filling the lock is merely getting it ready to lose its next lockful of water. The water comes from the reservoir above. It can't come from anywhere else (OK perhaps it has been raining really hard for a very long time!).

I understand what you're saying but, for it to be right, the boat would need to be sitting on the bottom of a lock totally devoid of water either before going up or coming down.

 

Keith

 

Correct.

[bassplayer]

I suppose the only factors we really need to worry about is that gravity and rain are free, but pumps aren't!

[Loafer]

[IanD]

For one lock on its own between two big pounds, there's a much easier way to think of this...

 

Assuming the lock is set for you -- going up or down -- you go into the lock and close the gates, no water "consumed" yet.

 

Then to change the level of the water in the lock to fill or empty it (with the boat floating in it) you have to move a volume of water in or out given by (lock area*lock rise).

 

Then you open the gates and sail out.

 

Amount of water moved is exactly the same in both cases, and has nothing to do with the displacement of the boat.

 

If the lock isn't set for you or there's a flight with small pounds (or a staircase) it's a bit more complicated...

[Loafer]

Approaching a flight of 5 going downhill. All locks empty.

 

You fill the top lock. 1 lockful from upper pound consumed.

 

You empty the top lock and motor out. The contents of your lock have added to the pound you're now in.

 

Fill the 2nd lock with the water you brought with you

 

Empty that into the next pound and so on.

 

Empty last lock and motor out, along with the lockful of water with which you originally filled the top lock. No more water has flowed into the system because the top lock is still empty.

 

Where am I going wrong with this?

[David Mack]

This is such an old chestnut! And it depends what you mean by "used". In my book water is used when it is taken from the reservoir or other source feeding high pounds, which on average (and ignoring other losses) must be equal to the amount lost at the bottom end of the canal (over weirs on sump pounds or into rivers to which the canal connects).

 

Consider a simple example:

 

A single canal, completely isolated, with one lock. At the start both pounds are on weir, the lock is full and the boat is in the upper pound.

 

1. Boat moves into lock. No change in water levels, no water runs over any weir and no topup is required. So no use of water.

2. Lock is emptied. One lockful of water drains into the lower pound and flows to waste over the weir.

3. Boat moves out into lower pound. No change in water levels, so no use of water.

4. For the return trip, the boat moves back into the lock. No change in water levels, no use of water.

5. Lock is filled from upper pound.

6. Boat moves out into upper pound.

7. 1 lockful of water is required from the reservoir to bring the upper pound back up to weir level.

 

We are now back in the same position as the start. Both pounds are full, the lock is full, both pounds are on weir. One lockful of water has been taken from the reservoir and one lockful of water has run to waste. So the overall water consumption for the round trip is one lockful.

 

The same is true if the boat starts in the bottom pound with the lock empty. But if the boat starts in the top pound with the lock empty, or in the bottom pound with the lock full, then a round trip takes 2 lockfuls of water to get back to the same state.

 

So if every boat encounters the lock in its favour (as in working turns) one lockful of water is used for an up and a down passage, and the average consumption per boat movement is half a lockful. But if every boat encounters the lock against it (as when a succession of boats are travelling in the same direction) then one lockful is used for each passage. So if traffic is even throughout the day, you can get close to half a lockful per boat, whereas if there is a tidal flow (mostly one way in the morning, and the opposite in the afternoon) you end up using virtually one lockful per boat.

 

In any real situation you will be somewhere between these two cases.

 

 

When doing these analyses, some people get worried that in descending a flight of locks which are all empty, when you empty the first lock into the full pound below the water runs to waste, but when you fill the second lock (assuming you haven't drawn the paddles before emptying the first lock) you leave the intermediate pound a lockful down. This represents a one-off waste of water only, rather than being a water cost for every passage. Because when the next boat coming down does the same, the water they let out of the top lock refills the intermediate pound, and this is then drawn off leaving that pound as they found it - one lockful down. So the subsequent passages don't actually waste this water.

 

 

One of the issues rarely considered is that whereas pleasure boats may be regarded as having constant displacement, a cargo carrying boat is not.

 

A long time ago I worked out the water consumption of two versions of the theoretical canal. In the first canal, boats are loaded at the end of the upper pound, proceed down the lock to the far end of the lower pound, where they are unloaded, and then proceed back to the start point empty.

 

The second canal is the other way round - boats are loaded in the lower pound and unloaded in the upper pound.

 

Taking into account the water which flows over the weir when the boat is loaded (and increases its displacement) and the water needed to bring the pound up to weir level when unloading takes place, as well as the water required for lockage, I concluded that carrying a load uphill requires more water than carrying it downhill - a conclusion which fits with energy considerations.

[Scholar Gypsy]

 

Energy is conserved without you even thinking about it.

 

When a body is partially or totally immersed in a fluid, it experiences an upthrust equal to the weight of fluid displaced. Mr Archimedes worked that one out a long time ago.

 

In other words, it doesn't matter whether it's a boat plus water, or just water, it's the same amount of potential energy (for that is what it is) that gets lost.

The energy 'lifting' the boat is exactly the same as the energy lost when the water comes down, whether or not there's a boat along for the ride.

...which is why your (3) and (4) are incorrect. It's the same volume of water, one lockful, regardless.

 

The energy argument is an interesting one, although I suspect it is not the most obvious way to prove the result.

 

• if you fill a lock with no boat in it then the volume of water flowing in from the upper pound (assumed to have infinite area) is V, and the potential energy released by the water flowing is 1/2 x (weight=volume x density x g) x h, where g is 9.8 m/s² and h is the height of the lock. (the factor 1/2 appears as the average amount the water falls is 1/2 h).
• This potential energy is converted into sound energy (which heats the atmosphere etc) and kinetic energy (turbulence) which as the water settles down is converted into heat energy, heating up the water (a bit).

• If the lock has a boat in then the same volume V of water flows in when the lock is filled, but the loss of potential energy of the water is slightly more, namely (1/2 x V + D) x g x density x h. This is because the "hole" the boat creates when the lock is empty is filled by the hole created when the lock is full
• this energy is converted into the same amount of sound and heat energy as before, and the excess amount (D x g x density x h) is accounted for by the increased gravitational potential energy of the boat, as it is lifted.

• and a similar argument when the lock is emptied

The answers to Q1 and Q2 are the same, but there is no reason why Q3 and Q4 should have the same answer. They are different questions...

This is such an old chestnut! And it depends what you mean by "used". In my book water is used when it is taken from the reservoir or other source feeding high pounds, which on average (and ignoring other losses) must be equal to the amount lost at the bottom end of the canal (over weirs on sump pounds or into rivers to which the canal connects).

 

Consider a simple example:

 

A single canal, completely isolated, with one lock. At the start both pounds are on weir, the lock is full and the boat is in the upper pound.

 

1. Boat moves into lock. No change in water levels, no water runs over any weir and no topup is required. So no use of water.

 

strictly speaking, the upper pound has more water in when the boat has moved into the lock, compared with before. So you've used a "negative" amount of water .... I follow the rest of what you say.

[Scholar Gypsy]

 

The energy argument is an interesting one, although I suspect it is not the most obvious way to prove the result.

 

• if you fill a lock with no boat in it then the volume of water flowing in from the upper pound (assumed to have infinite area) is V, and the potential energy released by the water flowing is 1/2 x (weight=volume x density x g) x h, where g is 9.8 m/s² and h is the height of the lock. (the factor 1/2 appears as the average amount the water falls is 1/2 h).
• This potential energy is converted into sound energy (which heats the atmosphere etc) and kinetic energy (turbulence) which as the water settles down is converted into heat energy, heating up the water (a bit).

 

I been worrying about the last couple of words here.

 

If I have my sums correct, then for a lock that has a 2m fall, and 2m depth when the lock is empty, and assuming all the energy is converted into heat (no noise), the temperature of the water in the lock will rise by about 1/1000 deg C when it is filled.

 

My next task is to compare this to the heat transferred via an effective skin tank during the three minutes the lock takes to fill.