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Broken paddle...


MtB

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Ok here's something that exercises my furry little brain once in a while, without me aver arriving at a conclusion.

Imagine a regular ordinary lock which has two top paddles and two bottom paddles, but one of the paddles is taped up, broken and out of action.

Does it take exactly twice as long to fill/empty this lock as it does when all the paddles are working? Or longer than twice as long? Or less than twice as long?

Please explain your workings. Many thanks.

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If it was just paddles in and out, then I would expect two being twice as fast as one.  However, we must consider the leaks as well.  So if the lock leaks only at the opposite end with the equivalent of (for example) half a paddle then with a single paddle open you would have a net gain of half a paddle out (the leak) and one paddle in (that you just opened) giving an overall half paddle.  With 2 paddles open, then it would be 2 (paddles open) less the half paddle leak, giving a net gain of 1.5 paddles.

So in this example a single paddle would be only 1/3 the speed of two paddles.

 

Of course with the equivalent of a single panel leak, the lock will never get more than half full with a single paddle open but will slowly fill with two paddles open.

 

Edited by Chewbacka
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On 13/12/2017 at 10:31, Chewbacka said:

If it was just paddles in and out, then I would expect two being twice as fast as one.  However, we must consider the leaks as well.  So if the lock leaks only at the opposite end with the equivalent of (for example) half a paddle then with a single paddle open you would have a net gain of half a paddle out (the leak) and one paddle in (that you just opened) giving an overall half paddle.  With 2 paddles open, then it would be 2 (paddles open) less the half paddle leak, giving a net gain of 1.5 paddles.

So in this example a single paddle would be only 1/3 the speed of two paddles.

 

 

Thank you for your workings. 

You have however, ignored the probability of there being leaks at both ends. 

Edited by Mike the Boilerman
Change 'their' into 'there'. Jeez!
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Bear in mind that the time taken to transit a lock is not only dependent on the time taken to "fill" it (or "empty" it). The number of paddles has an effect on how fast the water moves, but that is only one stage of the whole process. 

Time taken to:

A - Open gates, enter lock, close gates, walk to other end. move in

B - Draw both (or all) paddles, which only flow to maximum rate when fully drawn and the static pressure behind them (head) is at its greatest. The question is whether the relationship between flow rate and head is linear, and I suspect it isn't. 

C - Open gates, leave lock, drop paddles and close gates.

Only B changes if there is a paddle out of action. If B is usually five minutes, it will increase to no more than double, but the total transit time will be nothing like double.

3 minutes ago, philjw said:

Do we think that the leak from the bottom would be at a constant rate or does it increase as the depth of water in the lock increases?  Similar considerations might apply to any inward leak at the top.

And to the flow rates through the open paddles!

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14 minutes ago, Mike the Boilerman said:

 

Thank you for your workings. 

You have however, ignored the probability of there being leaks at both ends. 

If the leaks at both ends are exactly the same, they can be ignored - as in my earlier answer.  But if the leaks are different, then in one direction (for example going up) they will add to the open paddles which would make the fill faster, but in the other direction, slower.

So if you want to consider leaks at both ends, then without specifying the size of your leaks, it is impossible to answer your question.

Edited by Chewbacka
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26 minutes ago, Mike the Boilerman said:

 

Thank you for your workings. 

You have however, ignored the probability of there being leaks at both ends. 

You have also assumed that both paddles allow an equal amount of water into the lock.

How sure can you be that this is the case?

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Is this thread relevant on say the K and A? if it were on such as the lets say Trent and Mersey then tests could be done but as the locks are left unused on the K and A due to lack of boat movement no one knows to what extent leaking gates/paddles could influence the outcome.

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1 hour ago, Chewbacka said:

If it was just paddles in and out, then I would expect two being twice as fast as one.  However, we must consider the leaks as well.  So if the lock leaks only at the opposite end with the equivalent of (for example) half a paddle then with a single paddle open you would have a net gain of half a paddle out (the leak) and one paddle in (that you just opened) giving an overall half paddle.  With 2 paddles open, then it would be 2 (paddles open) less the half paddle leak, giving a net gain of 1.5 paddles.

So in this example a single paddle would be only 1/3 the speed of two paddles.

 

Of course with the equivalent of a single panel leak, the lock will never get more than half full with a single paddle open but will slowly fill with two paddles open.

 

Without leaks, it would take twice as long assuming both paddles are equally sized and positioned etc etc.

With leaks, it's a lot more complicated.  The rate of leakage depends on the pressure (head of water) either side of the hole so that its flow varies as the lock fills/empties.  With a half paddle drawn (or an equivalent leak)  at the lower end and a full paddle at the upper end, a dynamic equilibrium is reached with the lock 2/3rds full.  Which is usually too much to force open - so it will take forever.  Assuming the paddles are equally sized etc etc

When there is a normal-size leak at the lower end, the lock never fills in simple terms - it just gets close enough so that you can push the gate open against the remaining pressure.  On shortish pound the wave set up by drawing the paddles sharply can reflect back and give you a hand too.  

So the answer partly depends on your strength.

It gets even more complicated if you take account of the levels in the upper and lower pounds changing during the process.

 

 

 

 

 

Edited by Tacet
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1 hour ago, Dyertribe said:

You have also assumed that both paddles allow an equal amount of water into the lock.

How sure can you be that this is the case?

They will not, because one of them is broken! :P

1 hour ago, bizzard said:

Providing the top gates are sealing ok, a little less than twice as long, because the full weight of the water is concentrated on the one sluice instead of being divided between two.

Bad science!

(But I can't work out if you are having a laugh or not!)

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1 hour ago, Chewbacka said:

If the leaks at both ends are exactly the same, they can be ignored - as in my earlier answer.  But if the leaks are different, then in one direction (for example going up) they will add to the open paddles which would make the fill faster, but in the other direction, slower.

So if you want to consider leaks at both ends, then without specifying the size of your leaks, it is impossible to answer your question.

But with leaks at both ends, the rate of leakage will vary. Assuming going up, as the lock fills the leakage from the top will decrease while, once the bottom gates are fully closed, the leakage from the bottom will increase.

We once went up Atherstone when one of the top paddles was U/S on the bottom lock. There was a bit of a queue, as the lock was taking about 25 minutes to operate, and, even then, the top gate was very heavy. We managed to cut this down a bit by having half a dozen heavy people on the top gate ....

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28 minutes ago, Machpoint005 said:

Isn't the assumption a little too sweeping?

As an engineer the assumption is reasonable, as a scientist, it is a little unreliable but as a mathematician it is hopeless as there is no consideration of projections causing turbulance and friction etc etc etc.  I consider myself as an engineer, so am quite happy with approximations. 

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39 minutes ago, alan_fincher said:

They will not, because one of them is broken! :P

Bad science!

(But I can't work out if you are having a laugh or not!)

Yoo've not observed how water gushes out of the sluices have yoo..  Observe while someone else works the paddle gear.  One paddle open, water gushes out, open second paddle water gushes out. Water from first sluice lessens slightly as second is opened. Reverse the process, close one paddle, water gushes out more again from the one sluice.

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1 hour ago, Chewbacka said:

As an engineer the assumption is reasonable, as a scientist, it is a little unreliable but as a mathematician it is hopeless as there is no consideration of projections causing turbulance and friction etc etc etc.  I consider myself as an engineer, so am quite happy with approximations. 

I AM an engineer, so I recognise the difference between an engineering approximation and a guess!

25 minutes ago, bizzard said:

Yoo've not observed how water gushes out of the sluices have yoo..  Observe while someone else works the paddle gear.  One paddle open, water gushes out, open second paddle water gushes out. Water from first sluice lessens slightly as second is opened. Reverse the process, close one paddle, water gushes out more again from the one sluice.

Yes, that's my experience too.

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I think, because this is flow rate over an area, it will be 4 times faster.

If the area is considered to be P, the flow rate through P is a squared relationship. Thus when you have 2P the resulting flow rate will be 4 times greater.

The flow out due to leakage would exacerbate this I think, as it spends longer leaking because it spends longer filling.

There's also the pressure differential to consider - empty vs. nearly full lock

TO add: I'm ignoring the local drop in water height at the feed to the lock i.e. the drop in sluice discussion immediately preceding my post

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