K&A locks left empty?

[magnetman]

Calculus?

Maybe he will be able to find the answer with his pendulum. 

 

Edited August 31, 2021 by magnetman

[Scholar Gypsy]

1 hour ago, dmr said:

 

You experiment with canal water, me and mtb will experiment with cider, and then we can compare results.

 

I think a more intuitive version of your "gate" thinking is to place this thin gate (made from clingfilm) 1/4 along the pound, splitting it into a short and long pound, if there is a pressure difference (relating to distance from the locks), then the clingfilm will deform. However you are not thinking this through; if there is a pressure difference (without the gate) then the water must flow so as to equalise that pressure and so the gate will never see any pressure difference, what will happen is the pound will become a little deeper towards the locks and shallower at the middle. Now we do actually know this to be true, for example on the Oxford summit I can get into Napton and Claydon top locks without trouble but always run aground towards the centre of the pound

 

That 2/3 centre of action is not immediately intuitive, I have a horrible feeling it needs calculus to work that one out?????

 

Calculus is the obvious way of doing this. Using the notation of the video, the integral of y^2 (from 0 to h) is 2/3 x h x  the integral of y on the same interval. 

 

But one can prove this result using pure geometry. For any triangle, join each vertex to the mid point of the opposite side. The three lines you get all intersect at a common point (called the centroid), which is the balancing point (centre of gravity) of the triangle. Also, the centroid is 2/3 of the way along the line from the vertex to the opposite mid point. From this one can deduce that the centre of action of the force on a lock gate is 2/3 of the depth of the gate - the two problems are related. (Imagine a right angle triangle with the 90 degrees at water level and the other two corners at the two bottom corners of the gate). For a proof of the centroid theorem see here:

http://ceemrr.com/Geometry2/TriangleCenters/TriangleCenters_print.html

https://en.wikipedia.org/wiki/Centroid

Wikpiedia is rather unclear whether this result was found by Euclid or Archimedes, or three hundred years later by someone called Heron

[dmr]

35 minutes ago, Scholar Gypsy said:

 

Calculus is the obvious way of doing this. Using the notation of the video, the integral of y^2 (from 0 to h) is 2/3 x h x  the integral of y on the same interval. 

 

But one can prove this result using pure geometry. For any triangle, join each vertex to the mid point of the opposite side. The three lines you get all intersect at a common point (called the centroid), which is the balancing point (centre of gravity) of the triangle. Also, the centroid is 2/3 of the way along the line from the vertex to the opposite mid point. From this one can deduce that the centre of action of the force on a lock gate is 2/3 of the depth of the gate - the two problems are related. (Imagine a right angle triangle with the 90 degrees at water level and the other two corners at the two bottom corners of the gate). For a proof of the centroid theorem see here:

http://ceemrr.com/Geometry2/TriangleCenters/TriangleCenters_print.html

https://en.wikipedia.org/wiki/Centroid

Wikpiedia is rather unclear whether this result was found by Euclid or Archimedes, or three hundred years later by someone called Heron

 

I dunno, all I want to do is go boating and drink a bit of beer and here we are  talking centroid theorum, Euclid and Archimedes. Not heard of Heron before. Saw several today but don't think they were mathematicians,.

 

ahh, Heron was a Greek mathematician and engineer and invented that jet based steam engine that we have all seen pictures of, well before our Mr Watt.

[MtB]

46 minutes ago, dmr said:

ahh, Heron was a Greek mathematician and engineer and invented that jet based steam engine that we have all seen pictures of, well before our Mr Watt.

 

Scotland's Mr Watt, Shirley. 

 

Nearly all the good British engineers generally turn out to be scotch, once one looks properly innit. 

 

One of the few exceptions to this seems to be that jolly good chap IK Brunel.

[David Schweizer]

13 hours ago, MtB said:

 

Scotland's Mr Watt, Shirley. 

 

Nearly all the good British engineers generally turn out to be scotch, once one looks properly innit. 

 

One of the few exceptions to this seems to be that jolly good chap IK Brunel.

 

Scottish, Mike.

 

As my Aberdeen born mother always said "Scotch is Whisky (or pies/eggs), people from Scotland are Scottish"

[MtB]

3 minutes ago, David Schweizer said:

Scottish, Mike.

 

I knew I'd catch someone with that, lol!! 

And on a related note I notice peeps who seem to know about whisky, tend to avoid calling it "Scotch"...

 

 

[David Schweizer]

2 hours ago, MtB said:

 

I knew I'd catch someone with that, lol!! 

And on a related note I notice peeps who seem to know about whisky, tend to avoid calling it "Scotch"...

 

 

 

Good try!

[MtB]

3 hours ago, David Schweizer said:

 

Good try!

 

Have you not noticed my posts are littered with little hooks like that, for poeple to bite on? 

[Mike Todd]

4 hours ago, David Schweizer said:

 

Good try!

Perhaps because they don't want to admit to drinking whiskey

[furnessvale]

6 hours ago, David Schweizer said:

 

Scottish, Mike.

 

As my Aberdeen born mother always said "Scotch is Whisky (or pies/eggs), people from Scotland are Scottish"

I always have a scotch available to slip under my lorry wheel on hills.  Not adverse to using a person from Scotland instead though he may object!