Why don't lock gates leak (theoretically)

[Scholar Gypsy]

 

^{Unfortunately not... I'm one of those miserable specimens who lie there dog tired at the end of the day for 2 - 3 hours with the brain rattling away at full speed. I then drop of for an hour or two before then waking up again, brain still going for the rest of the night. I think I've felt tired constantly for about thirty years now and it ain't pleasant. Over the years I've tried just about every remedy known and nothing seems to work...}

 

^{Besides - sad old git that I am I now can't wait to see the forces diagram that's been promised by Scholar Gypsy!}

 

 

^{I'm a sad old git who spends most of his time fighting to stay awake. The wife on the other hand spends her sleeping hours mainly awake. ...... So, in the morning I let her have a lie in (and I use the 'free period' to set the world to rights, only in at the moment I'm thinking 'lock gates'!:-)}

 

I wouldn't want to get too involved with Scholar Gypsey's force diagram as he appears to be a bit anally retentive at the moment

 

I always thought lock gates designed to be effectively self sealing. What impresses me is that within the differing circumstances they encompass, they remain true! By which I mean they flex and twist yet they stick together till torn asunder.......

 

^{I am not sure I would agree with "at the moment" - with apologies to Pelican, I suspect I am always like this.}

 

^{I am also not sure if I can solve Pen n Ink's insomnia, This problem will require some more thought and also a three dimensional approach. Even if one assumes a weightless, perfectly rigid and fitting gate (so the forces at the mitre are zero) I have not yet got a solvable set of equations. I have remembered how to show that the pressure from the water on the gate acts (in effect) at a point 2/3rds of the way down from the water level to the bottom of the gate. I had better save this for a weekend task....}

[Doorman]

I believe that Scholar Gypsy was alluding to what's termed as coplaner forces. Whereby two or more forces act upon an object and cause a resultant force elsewhere.

 

In the case of the mitre gates, the pressure from the head or differing level of water, acts upon the gates perpendicular to their sides and thus exerts a force upon the leading edges where they meet once closed. The meeting of the gates forms a fulcrum and this in turn allows a resultant force along the length of the gates thus pressing them against the quoin. The greater the depth if water -or head- the greater the force against the leading and trailing edges of the gates.

 

You may notice how the top collar on lock gates is left quite loose, this, I presume, is to allow sufficient movement of the trailing edge to allow it to mesh into the quoin from the resultant force.

[Scholar Gypsy]

^{I am also not sure if I can solve Pen n Ink's insomnia, This problem will require some more thought and also a three dimensional approach. Even if one assumes a weightless, perfectly rigid and fitting gate (so the forces at the mitre are zero) I have not yet got a solvable set of equations. I have remembered how to show that the pressure from the water on the gate acts (in effect) at a point 2/3rds of the way down from the water level to the bottom of the gate. I had better save this for a weekend task....}

Thinking some more while cycling home.

 

We know where the water pressure acts on the gate - midway between mitre and heelpost, two thirds of the way down.

 

To consider an over-simplified situation, if we imagine the lock structure (cills, quoin, mitre, hinge etc) is in contact with the gate at precisely 3 points, then we can work out what the reaction forces are that hold the gate in place. This is essentially the same problem as supporting any object with a flat bottom on three (horizontally) coplanar points (assuming the centre of gravity is within the triangle).

 

An example is worked out here - with the gate held in place just in three places - top and bottom of the hinge, and midway up the mitre. One can then work out all the forces, as a multiple of the pressure force. This includes the transverse forces along the gate - the source of the original sleeplessness I think?

 

This is of course not reality, though you could simulate this situation on the Nene by wedging a large solid object between the upper gates, half way down, on one of the few remaining locks that are not electrified, and then opening the guillotine bottom gate).

 

In reality, if there are more than three contact points (or even worse contact surfaces along the edges of the gate) then one cannot use this sort of technique - there is not enough information to get a solvable set of equations (cf a flat object supported on four or more coplanar points). The precise solution will depend on how the gate flexes under pressure, and would only be solvable using some quite complex computer modelling, I fear, to calculate the stress and strain within the gate.... It would be quicker to measure the forces in play on an actual gate ...

 

I hope this helps, but rather doubt that it does.

Edited October 11, 2013 by Scholar Gypsy

[pelicanafloat]

My thinking....

 

Place a plug in the basin. A leak occurs if the water in the high pressure area can drip into the lower pressure area.

A tap without a washer. The two surfaces unable to mate successfuly, hence a pressure drop - leak occurs. Solution, place a rubber deformable washer between the two faces. The edge of the washer can take up the deformity and the pressure is contained.

Lock gate... The gate acts as a rigid but flexible structure. The pressure on a typical pair of gates in the /\ position is such that the force triangle can be resolved parallel to, and at right angles to the lock. The 'right angled' force has to balance out unless the gates are open, which doesn't apply, or, the system is in balance and held rigid.Therefore, the gates are effectively pushed against each other, in the middle, and against the lock housing at the hinged section. If no pressure loss, then the gates don't leak. If a hole appears, there is a pressure loss that allows water to move through the area. This action will cause a pressure gradient in the locality and this will act upon any moveable material effectively to suck it into the low pressure area; the lock gate being able to flex, will also be sucked hence it is pulled into the lock housing by the difference in pressure... I also assume this is the reason why the lock hinges are 'loose' - they allow the gates to flex.

[Pluto]

If you are interested in the theoretical side of lock design, there are quite a few engineering books on the subject, particularly in Dutch and German. However, locks in the UK were generally built by craftsmen who seem to have solved the problems without needing the mathematics used by today's academically-trained engineers. It is a pity academics and politicians today undervalue such practical experience. The only late18th and early 19th century engineer with academic qualifications was I K Brunel, and his work tended to be a failure in practise, with little that made a profit.

[pelicanafloat]

If you are interested in the theoretical side of lock design, there are quite a few engineering books on the subject, particularly in Dutch and German. However, locks in the UK were generally built by craftsmen who seem to have solved the problems without needing the mathematics used by today's academically-trained engineers. It is a pity academics and politicians today undervalue such practical experience. The only late18th and early 19th century engineer with academic qualifications was I K Brunel, and his work tended to be a failure in practise, with little that made a profit.

 

Actually, the craftsmen of old, were taught a very high level of applied mathematics in their course work. It might not come out as figures so much as a thorough understanding of the mechanics involved. The ability to form complex roof structures, and stairflights, an ability in this case applicable to a skilled carpenter, but equally other trades with their own levels of abilty. A craftsman was taught his trade, and he used his learning to teach others. Yes, it is a shame that the satisfaction obtained from understanding the materials you are working with no longer seems important...

[Pen n Ink]

[.......]

 

I hope this helps, but rather doubt that it does.

 

Oh Dear!

 

Now I'm no advanced mathematician (bailed out of 'A' level Maths and Further Maths three quarters of the way through!) but.. I can follow the thinking as far as F-H=P/3, and whilst I don't fully understand the next two equations, I don't think they have any bearing on X, Y and Z which are the critical forces here, what I really don't understand is the equation which suddenly introduces tan theta into the mix; If P is acting perpendicular to the gate, then H, F and M are also perpendicular to the gate. This means that angle MX is 90 degrees, and X must = 0; a force (in this case P) acting perpendicular to a plane cannot introduce any sideways force, surely? We can definitely accept that X = Y + Z otherwise the gate would blow itself apart, but that is entirely a different thing, being forces within a solid object which, timber tension excepted, will be zero?

 

 

Actually, the craftsmen of old, were taught a very high level of applied mathematics in their course work. It might not come out as figures so much as a thorough understanding of the mechanics involved. The ability to form complex roof structures, and stairflights, an ability in this case applicable to a skilled carpenter, but equally other trades with their own levels of abilty. A craftsman was taught his trade, and he used his learning to teach others. Yes, it is a shame that the satisfaction obtained from understanding the materials you are working with no longer seems important...

 

Sorry - posted while I was trying to get my head around the equations!

 

You are absolutely right here. The years I have spent around carpenters and joiners, and building staircases myself, have taught me that your average joiner is still quite a capable mathematician. Personally, my crowning glory has been the construction of a number of (timber) full 180 degree turn curved staircases which are completely unsupported in the centre (no newel post) and despite all intuition to the contrary, they've stayed put!

[Scholar Gypsy]

My thinking....

 

Place a plug in the basin. A leak occurs if the water in the high pressure area can drip into the lower pressure area.

A tap without a washer. The two surfaces unable to mate successfuly, hence a pressure drop - leak occurs. Solution, place a rubber deformable washer between the two faces. The edge of the washer can take up the deformity and the pressure is contained.

Lock gate... The gate acts as a rigid but flexible structure. The pressure on a typical pair of gates in the /\ position is such that the force triangle can be resolved parallel to, and at right angles to the lock. The 'right angled' force has to balance out unless the gates are open, which doesn't apply, or, the system is in balance and held rigid.Therefore, the gates are effectively pushed against each other, in the middle, and against the lock housing at the hinged section. If no pressure loss, then the gates don't leak. If a hole appears, there is a pressure loss that allows water to move through the area. This action will cause a pressure gradient in the locality and this will act upon any moveable material effectively to suck it into the low pressure area; the lock gate being able to flex, will also be sucked hence it is pulled into the lock housing by the difference in pressure... I also assume this is the reason why the lock hinges are 'loose' - they allow the gates to flex.

 

Yes, I think I agree with that. It is worth noting that there are some lock gate designs - eg the radial gates at Limehouse - where the gates are held in place via a vertcal pillar, and the forces in play at the top bottom and centre seals are essentially minimal. So you could remove all the rubber seals on that lock and the gates would not collapse, though they would leak rather a lot eg through the inch or two gap between the gates. With mitre gates the gates do need to be in contact, otherwise they will collapse.

 

Oh Dear!

 

Now I'm no advanced mathematician (bailed out of 'A' level Maths and Further Maths three quarters of the way through!) but.. I can follow the thinking as far as F-H=P/3, and whilst I don't fully understand the next two equations, I don't think they have any bearing on X, Y and Z which are the critical forces here, what I really don't understand is the equation which suddenly introduces tan theta into the mix; If P is acting perpendicular to the gate, then H, F and M are also perpendicular to the gate. This means that angle MX is 90 degrees, and X must = 0; a force (in this case P) acting perpendicular to a plane cannot introduce any sideways force, surely? We can definitely accept that X = Y + Z otherwise the gate would blow itself apart, but that is entirely a different thing, being forces within a solid object which, timber tension excepted, will be zero?

 

 

Sorry - posted while I was trying to get my head around the equations!

 

You are absolutely right here. The years I have spent around carpenters and joiners, and building staircases myself, have taught me that your average joiner is still quite a capable mathematician. Personally, my crowning glory has been the construction of a number of (timber) full 180 degree turn curved staircases which are completely unsupported in the centre (no newel post) and despite all intuition to the contrary, they've stayed put!

 

Sorry, I am indeed a mathmo rather than an engineer (and my foreign languages are essentuially useless). And I am a fairly useless carpenter.

 

The equation with tan theta is there because the force between the gates is actually across the lock - ie at 90 degrees to the axis of the lock. One way of justifying this statement is to recall (Newton's laws) that the contact force gate A exerts n gate B is equal and opposite to the force gate B exerts on gate A, and then to apply symmetry. I need to draw a plan view of the lock to explain why tan(theta) = M/X.

 

In the diagram. X Y and Z act in the plane of the gate, MH F and P are perpendicular to the gate.

 

As the angle theta gets smaller, the forces X Y and Z get bigger, which creates challenges for the carpenter and for the mason. On the other hand if you increase the angle you need more wood fo the gate, and more space to fit longer balance beams...

[Pluto]

snip

As the angle theta gets smaller, the forces X Y and Z get bigger, which creates challenges for the carpenter and for the mason. On the other hand if you increase the angle you need more wood fo the gate, and more space to fit longer balance beams...

Changing the angle of the mitre only varies the individual forces on the quoin and sill. The total force remains the same if the water level remains the same, with the part tending to push the walls aside varying with the force tending to push the walls/gates towards the lower end of the lock. The actual angle of the mitre does vary from canal to canal, for example the C&HN gates are narrower than those on the L&LC. Constructing lock walls sufficiently strong was always a problem for early canal builders. The first locks on the Canal du Midi had straight sides, but due to the failure of one wall, the remaining locks were built with curved sides. The Rochdale Canal had continual problems with lock structures as the canal had been built on the cheap. As so often with engineering, it is a balance between knowledge and cost. Early constructors tended to overbuild to accommodate their lack of detailed knowledge, and to provide an adequate factor of safety.

[Pen n Ink]

And this is supposed to help me sleep?!!! I love this forum for the random knowledge and wisdom lurking beneath the surface, but I think it's going to take me a while to digest the last two posts. Got to do some work at some point as well...

[Scholar Gypsy]

Changing the angle of the mitre only varies the individual forces on the quoin and sill. The total force remains the same if the water level remains the same, with the part tending to push the walls aside varying with the force tending to push the walls/gates towards the lower end of the lock. The actual angle of the mitre does vary from canal to canal, for example the C&HN gates are narrower than those on the L&LC. Constructing lock walls sufficiently strong was always a problem for early canal builders. The first locks on the Canal du Midi had straight sides, but due to the failure of one wall, the remaining locks were built with curved sides. The Rochdale Canal had continual problems with lock structures as the canal had been built on the cheap. As so often with engineering, it is a balance between knowledge and cost. Early constructors tended to overbuild to accommodate their lack of detailed knowledge, and to provide an adequate factor of safety.

 

Sorry, but I don't think that is correct. There is a difference between the net resultant force exerted by the water in the uphill pound on the lock and surrounds, which is constant, and the detailed forces within and between the elements (whuich is what would make a structure fail).

 

In my simplified model, if the angle theta increases, then the size of the gate increases (proportional to 1 / cos(theta) ) and so the total pressure force increases. The end result is that the forces perpendicular to the gate are proportional to (1 / cos(theta)), and the forces along the gate are proportional to 1 / sin (theta) - which will get very large as theta gets smaller.

[John Williamson 1955]

Now, could someone tell me why the bottom of the gates don't leak (much)? The only "flexible" seal I normlly see on them is a piece of timber.

 

Bye!

 

John.

[IanM]

Now, could someone tell me why the bottom of the gates don't leak (much)? The only "flexible" seal I normlly see on them is a piece of timber.

 

Bye!

 

John.

 

Timber squishes* a bit so both bits seal against each other. Get something trapped in there and you soon see they don't seal

 

*technical term

[pelicanafloat]

 

Timber squishes* a bit so both bits seal against each other. Get something trapped in there and you soon see they don't seal

 

*technical term ..... don't you mean ...... *technical squirm

That sounds like the good old days of bribery when the Drainage Inspector would come out with instructive missives such as "and what if a ten pound note got trapped in there, would I pass it? I think not!" ...

[Pen n Ink]

As a joiner I'm just loving this idea of 10" x 10" oak "squishing"... or indeed flexing measurably over a 4' length!

[IanM]

As a joiner I'm just loving this idea of 10" x 10" oak "squishing"... or indeed flexing measurably over a 4' length!

 

Best you go and look at some lock gates with pressure on them then.

[IanD]

 

Timber squishes* a bit so both bits seal against each other. Get something trapped in there and you soon see they don't seal

 

*technical term

For us at Salterhebble top lack it was a truck tyre...

[John Williamson 1955]

As a joiner I'm just loving this idea of 10" x 10" oak "squishing"... or indeed flexing measurably over a 4' length!

If you work out the forces holding a lock gate shut, then oak "squishing" a fraction of an inch isn't so unimaginable.

 

I daresay they use something softer ( pine, maybe? ) as the sealing surface on the sill, although I've never really felt the urge to inspect the seal close up.

 

Bye!

 

John.

[Pluto]

 

Sorry, but I don't think that is correct. There is a difference between the net resultant force exerted by the water in the uphill pound on the lock and surrounds, which is constant, and the detailed forces within and between the elements (whuich is what would make a structure fail).

 

In my simplified model, if the angle theta increases, then the size of the gate increases (proportional to 1 / cos(theta) ) and so the total pressure force increases. The end result is that the forces perpendicular to the gate are proportional to (1 / cos(theta)), and the forces along the gate are proportional to 1 / sin (theta) - which will get very large as theta gets smaller.

But you still have the same amount/depth of water in the lock, so the total force it creates remains the same. It is the proportion between in line and transverse forces which vary.

Lock gates tend not to leak from the sill, unless something is trapped there, because when installed the gates are fitted to be flush with the sill and to meet at the mitre. The mitre joint should taper slightly such that there is a progressively larger (perhaps quarter inch max) gap above. The gates then twist slightly as the lock fills to make this gap watertight. As the mitre wears, the joint can be improved by running a saw down the seal.

[IanM]

If you work out the forces holding a lock gate shut, then oak "squishing" a fraction of an inch isn't so unimaginable.

 

I daresay they use something softer ( pine, maybe? ) as the sealing surface on the sill, although I've never really felt the urge to inspect the seal close up.

 

Bye!

 

John.

 

Indeed. We're not talking compressing to half its size, just enough 'squish' and flex to take up any small differences in the mating surfaces.

[Pen n Ink]

If you work out the forces holding a lock gate shut, then oak "squishing" a fraction of an inch isn't so unimaginable.

 

[...]

 

Oh I quite agree... fractions of a fraction, but I did use the word 'measurable' advisedly in the context

 

I really don't think that the amount that oak might "squish" under the relatively low pressures exerted by a lock gate (compared to point loads) is likely to have much effect on any seal which is being achieved at the hinge side of a gate, which was my original point... Just as a matter of interest has anyone worked out what the load is on the bottom edge of a gate at a given depth? I suspect that in psi type terms it isn't actually as great as you might think.

[IanM]

True, but still wouldn't like to get my finger caught in there though

[Scholar Gypsy]

 

Oh I quite agree... fractions of a fraction, but I did use the word 'measurable' advisedly in the context

 

I really don't think that the amount that oak might "squish" under the relatively low pressures exerted by a lock gate (compared to point loads) is likely to have much effect on any seal which is being achieved at the hinge side of a gate, which was my original point... Just as a matter of interest has anyone worked out what the load is on the bottom edge of a gate at a given depth? I suspect that in psi type terms it isn't actually as great as you might think.

 

For a lock gate 2m deep and 3m wide, the total force from water pressure (P in my picture ...) is equal to a weight of 3 tonnes (Force = g.density.Area.height/2) where g = gravity and density is 1 tonne per cubic metre. That gives you an idea of the scale of the forces involved, both those holding the gate in place against the pressure, and also the lateral forces in the plane of the gate.

 

So to answer the question, to get a rough idea of scale a 1 tonne force distributed though a sealing strip of oak 3m x 33mm is 10,000 Newtons through an area of 0.1 m2, which is 100,000 Pascals or about 15 psi. That's nearly 800 mm of mercury, so not good for the circulation in any trapped extremities ...

Edited October 11, 2013 by Scholar Gypsy

[Doorman]

Refreshing to see calculations in metric measurements rather than antediluvian imperials...........

[bizzard]

A chap went into a timber merchants to buy some wood.

Customer;--- I need a length of 4''x2'' Pine please.

Merchant;--- Ooooh! no sir I'm afraid not gov we don't do timber in those old sizes anymore we've gone all metric now yer know, yer need to come up to date don't yew. However 4''x2'' is about just under 10cmx5cm gov and if you be wanting any its £1-3-6d per foot.