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The result will also depend upon whether the paddles were lifted at exactly the same time, or whether there was only one person working them, in which case the second would be opened a short time after the first. This will affect the flow as the head, both above and below the paddles, will have changed.

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5 hours ago, Machpoint005 said:

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.

And to the flow rates through the open paddles!

Mike asked how long to fill the lock not how long to transit it!

5 hours 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.

If a paddle is say 1m below water level I can't see that the rate at which water goes through it will be affected by whether another paddle is open a few metres away....... but then again if the water level just above the top gates dropped a bit may be it would make a difference ..........?

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4 hours ago, Tacet said:

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

 

4 hours ago, Machpoint005 said:

Isn't the assumption a little too sweeping?

Well, as a first approximation, I didn't think so.  Broadly speaking, the rate of flow will be twice with two, identical paddles drawn than with one.

It will be wrong if you take into account relatively minor factors - such as if it's raining or the possible interaction of the two paddles in changing the flows or the additional restriction imposed by a narrows above the lock or the temporary lowering of the upper pound through drawing off, but that's getting a bit precise for me.

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5 hours ago, ditchcrawler said:

And if the leak is big enough it will never fill

As the second one down at Meaford has been close to proving all summer.

A shaft down the bottom mitre and an Atherstone wedge in the top gate have been most useful accessories!

George

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7 hours 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.

I would suggest, yer 'onor, that this depends on the paddles. Two ground paddles where the outfall into the lock face each other I can see some small reduction when the second paddle opens. Two paddles feeding one culvert (some of the narrow Trent and Mersey locks) I can definitely see the second one not doubling the flow, but two top gate paddles, as at Towney Lock, where the outlets are several feet above lower water level? Not so much...

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5 hours ago, Pluto said:

The result will also depend upon whether the paddles were lifted at exactly the same time, or whether there was only one person working them, in which case the second would be opened a short time after the first. This will affect the flow as the head, both above and below the paddles, will have changed.

 

This is one of the factors I chose not to mention in my OP!

Bizz earlier, I think was just being mischievous with his misleading comment about water pressure being concentrated on the one sluice. He knows better than that and is just stoking up debate. As am I ;)  

P.S. I was expecting his Normanship to have weighed in by now. But sadly I'm wrong.

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Everything else being exactly the same, and only two paddles of the same size (as the only variables to consider), I think it will take twice as long to fill if only one paddle is used.

This is because the flow of water through an underwater orifice is proportional to the area of opening. So one paddle means half the area and therefore half the flow - and thus twice as long to fill. 

Simple formula:     Water flow, Rec-Sub-Orifices.gif    Where A is the area (of the open paddle), and H is the difference in water levels (at the gate).

For more info, and a live calculator to put your own numbers in, have a look at  Water flow through a submerged hole.    

As an aside, to avoid unnecessary waiting, open the gate before closing the paddles.

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Yes it is definitely a good idea to shut the gates before closing the paddles especially where there are two gates because otherwise as you close one gate the water flow will cause the opposite gate to swing open.

However this does ignore the effect that the water flow to the lock on a canal is slightly restricted so that opening the second paddle causes the water level to drop slightly thus reducing the head across the first paddle. Hence it takes slightly longer than half the time with 2 paddles open, although if you include the effects of a slight leak at the other end which could make it take slightly less than half the time, the overall answer has to be:

The time will be the same or different, and if it is different it will be either greater or less.

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On 13 December 2017 at 11:28, mrsmelly said:

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.

I think you are doing the K and A boating community a dis-service. There are some, particularly in the continuous cruising community, who regularly wind paddles up and down, and swing lock gates open and closed, as a form of exercise. It does save on gym membership fees, you know!

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On 12/13/2017 at 16:28, NickF said:

Mike asked how long to fill the lock not how long to transit it!

Perhaps we should ask why he wants the lock full if he isn't going to transit it?

13 hours ago, Horace42 said:

Everything else being exactly the same, and only two paddles of the same size (as the only variables to consider), I think it will take twice as long to fill if only one paddle is used.

This is because the flow of water through an underwater orifice is proportional to the area of opening. So one paddle means half the area and therefore half the flow - and thus twice as long to fill. 

Simple formula:     Water flow, Rec-Sub-Orifices.gif    Where A is the area (of the open paddle), and H is the difference in water levels (at the gate).

For more info, and a live calculator to put your own numbers in, have a look at  Water flow through a submerged hole.    

As an aside, to avoid unnecessary waiting, open the gate before closing the paddles.

Not a lot of help without units - I suspect from the weird coefficients that you are in imperial!

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3 hours ago, Machpoint005 said:

Perhaps we should ask why he wants the lock full if he isn't going to transit it?

Not a lot of help without units - I suspect from the weird coefficients that you are in imperial!

I don't know. I copied the formula from the link. All the units are in the link and you pick the ones you like - for use in the calculator.

But whatever ones are used, they will cancel out when the ratio of flow rates are is calculated, so that you are left with a dimensionless number that can be used to calculate the time to fill the lock. 

Even so, without calculating anything, by looking at the formula it can be seen that the flow is proportional to area A of the opening, (the area of one or two paddles in this case) - assuming the same size then two paddles open should fill the lock in half the time. Or put the other way it should take twice as long with only one paddle open.

 

 

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18 hours ago, Horace42 said:

Everything else being exactly the same, and only two paddles of the same size (as the only variables to consider), I think it will take twice as long to fill if only one paddle is used.

This is because the flow of water through an underwater orifice is proportional to the area of opening. So one paddle means half the area and therefore half the flow - and thus twice as long to fill. 

Simple formula:     Water flow, Rec-Sub-Orifices.gif    Where A is the area (of the open paddle), and H is the difference in water levels (at the gate).

For more info, and a live calculator to put your own numbers in, have a look at  Water flow through a submerged hole.    

As an aside, to avoid unnecessary waiting, open the gate before closing the paddles.

But Horace I would argue that H will be less if you are drawing from two paddles as the drop in water level that occurs just above the top gates of a lock when you open the paddles will be greater if two paddles are being used at once.

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8 minutes ago, NickF said:

But Horace I would argue that H will be less if you are drawing from two paddles as the drop in water level that occurs just above the top gates of a lock when you open the paddles will be greater if two paddles are being used at once.

Yes, you could be right, but as H is the difference in water levels (at that instant), then a drop in the top level marginally slows the flow rate, and therefore takes longer to fill, but in doing so, water in the lock (at that instant) is now lower than before, therefore causing a marginally higher flow rate.

The marginal effects on the level might cancel out, giving the H as before. I don't know for certain, but I would guess they do. However, the OP did not ask for the exact time to fill the lock with one or two paddles - just a ratio - ie, twice as long with only one paddle open.

If the exact time is required it needs a lot more details. 

 

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38 minutes ago, cuthound said:

This thread makes my head hurt.

 

This was my dastardly plan in starting the thread :giggles:

4 hours ago, Horace42 said:

However, the OP did not ask for the exact time to fill the lock with one or two paddles - just a ratio - ie, twice as long with only one paddle open.

 

As a single hander, I can't open both paddles at the same time so one paddle open should empty/fill the lock is slightly less than twice the time both paddles would take, when there is no gate leakage.

Your calculations however, fail to take into account gate leakage which is significant on most locks these days.

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I gave Horace42 a green thing for introducing a bit of science. The relationship between rate of flow, head of water and area of opening confirms that the lock will in theory fill in twice the time with the assumption that the paddles are the same size.

However this doesn't hold true with the effects of leakage at the bottom gates. Bottom gate leakage has more effect than top gate leakage when filling a lock. This is true even where the leakage at top and bottom gates is the same at the same head of water. A change in head of water has a different effect on the rate of flow than a change of area. This is seen in the formula. The result is that in practical terms the lock will take slightly more than twice as long to fill.

I have tested this with some numerate examples (units are not a factor). The results also emphasise the realism about pushing against the pressure difference before a level is reached.

JP

Edited by Captain Pegg
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14 minutes ago, Captain Pegg said:

The relationship between rate of flow, head of water and area of opening confirms that the lock will in theory fill in twice the time with the assumption that the paddles are the same size.

 

Unfortunately this seemed so obvious to me I expected discussion to immediately revolve around the effects of gate leakage, timing of paddle opening and a few other minor factors I've forgotten for now!

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Before doing any trials it is necessary to define what you mean by a lock being "full".  The filling process slows down exponentially (ish) so that in fact a lock is never totally full. It is necessary to define full arbitrarily as when the fill rate has dropped to a certain level, say 1% of the total capacity of the lock when it was new. (Has this thread been sitting too close to another thread?)

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7 hours ago, Horace42 said:

Yes, you could be right, but as H is the difference in water levels (at that instant), then a drop in the top level marginally slows the flow rate, and therefore takes longer to fill, but in doing so, water in the lock (at that instant) is now lower than before, therefore causing a marginally higher flow rate.

The marginal effects on the level might cancel out, giving the H as before. I don't know for certain, but I would guess they do. However, the OP did not ask for the exact time to fill the lock with one or two paddles - just a ratio - ie, twice as long with only one paddle open.

If the exact time is required it needs a lot more details. 

 

Oh Horace this causes further confusion in my brain. Your argument would hold true for ground paddles or gate paddles which are fully submerged on both sides but I was thinking more of gate paddles discharging into a deep empty lock and so discharging into air not water .... then we need one set of ratios for discharge into air and one for discharge into water further complicated by the fact that as the lock fill the paddles will then be discharging underwater and we revert to the situation you describe. 

My answer to the OP therefore is "I don't know ... too confusing" 

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