Tuesday, November 20, 2012

Something I bet you never realised

Well I didn’t anyway.  Did you know that it takes more water for a boat to go up in a lock, than it does to go down?

I can see it now, but only because I read a section in Inland Waterways of Great Britain and Ireland (see yesterday’s post).

It quotes an essay by Mr W O’Brien which won the Canal Association prize in 1858.  Its a bit wordy and long winded so I’ve simplified the text and used more modern mathematical language.

The loss of water caused by the passage of a boat through a lock is as follows:-
Let W = the loss of water,
Let L = a lockfull of water as calculated by the surface area x the depth of rise or fall
Let B = the volume of water displaced by the boat.
When the boat ascends, the loss of water W= L+B
When the boat descends, W= L – B

Hmmm. You see when the boat comes into the bottom of a lock it pushes out B amount of water.  The lock fills with L gallons, then when the boat leaves the top of the lock another B gallons is drawn in from the canal above the lock. So it has used up L+B.

Going down.  The boat gives back B gallons to the canal above as it comes in, so the lock has L-B galloons in it, which is what is lost when it drops. I think that’s what it implies anyway.

That being so, we ought to have canals designed by M C Escher so we’re always going down hill.

Or thinking of it another way, shallow drafted boats like Herbie are cheaper (in water terms)  than deep boats like the coal boats Ara and Archimedes going uphill, but it’s the other way round going down.  Good innit?

Oooh, I just noticed that this is my 1006th post!! What a pity I missed out on doing a special thousandth edition.  Aah well, when we get to 2000 I'll do one.


Rainman said...

I think when the boat ascends W=L. It only takes L-B to fill to fill the lock, but then B is added when the boat leaves the lock ie L.

Oakie said...

Surely, if the boat displaces B when it enters the lock, it replaces B when it leaves, so the amount of water in the lock does not change, whether rising or falling. Correct me if you think I am wrong Archimedes!

Rick said...

On a similar thought:
If a boat goes goes down the Anderton Lift but no boat goes goes up, is water pumped uphill?