A little boating puzzle.

fergal.b

How much less water is required to pass a large boat through a lock than a small boat? To be more precise,consider two lakes at different elevations,connected by a lock.A boat enters through the open lock gate in the lower lake,and the gate is closed.The lock chamber is filled with water from the upper lake.Then the upper lock gate is opened,and the boat can continue its voyage.Compare two such passages of a boat through the lock.In one case the total mass of the boat is 50 tons.and in another case the mass is only 5 tons.How much more water,expressed in cubic meters,has to flow into the lock from the upper lake when the small boat passes through the lock than when the larger boat passes through?Or if your not good at maths, more water, less or the same. Or just name the lock.

FoxT

Suppose the lock has no boats in it, and the lower gates are shut. The lock is now at its lowest level, and contains x tons of water.

The upper sluices are opened & the lock fills up to the level of the higher lake. It now contains x+y tons of water.

Now, lets introduce a boat.

Boat weight is K tons.

Boat enters lower lock, and the gates are shut.

What is in the lower lock?

Answer: K tons of boat + x-K tons of water.

ie - total is x tons, as before.

Sluices are opened & the water level is raised to the level of the upper lake. The total contents of the lock now weigh x+y tons, as before.
So , no matter what the displacement of the boat is, it takes the same amount of water each time.

I have no idea where the lock is, though

-FoxT

fergal.b

What if one of the boats is a half submerged submarine.:D

FoxT

fergal.b wrote: »

What if one of the boats is a half submerged submarine.:D

huh?
doesnt matter!

Assuming no boat runs aground, It doesnt matter if it is the Star Trek Enterprise, a half submerged submarine, a fully submerged submarine, a Massey Ferguson tractor, or a sex toy...

Total weight in lower lock always = x tons. ( What would happen if it was heavier? or lighter? How could the lower lock water level differ from the level of the lower lake? )

Total amount of water consumed in locking up always = y tons.


Whats on my mind though, is, where is the lock pictured?

-FoxT

Shane Slv

The total weight in the lock will always be the same, but the amount of water in the lock would depend on the weight of the boat. A 50t boat will displace 50 tones of water so their would be 50000 liters less water in the lock then when empty and if a 5t boat was in the lock their would be 5000 less liters of water then when empty.

oscarBravo

Shane Slv wrote: »

The total weight in the lock will always be the same, but the amount of water in the lock would depend on the weight of the boat. A 50t boat will displace 50 tones of water so their would be 50000 liters less water in the lock then when empty and if a 5t boat was in the lock their would be 5000 less liters of water then when empty.

Right, but: imagine for a moment that the lock is filled up without any boat in it. The volume of water that's transferred from the upper lake is the surface area of the lock between the gates, multiplied by the difference in heights of the lakes.

Now, imagine the other extreme - a boat that completely fills the lock, displacing all the water in it when it's empty, but just barely floating a millimetre off the bottom of the lock. The amount of water in the lock is effectively zero. To raise that boat to the height of the upper lake, the amount of water that must be transferred in is the surface area of the lock multiplied by the difference in heights.

Ergo, the same amount of water is required no matter the displacement of the boat.

fergal.b

Too easy for you.
Intuitively one might think that more water is needed in the case of a small boat, but in Infact the amount of water is the same,irrespective of the size of the boat.A simple argument is as follows. The boat has entered the lock chamber,and the lower lock gate is open.Then the water levels in the chamber and in the lower lake are the same.We now close the lower gate,so that both gates are closed.Suppose that the difference in elevation between the two lakes is 2m.We can raise the level of the water in the lock chamber to that of the upper lake by inserting a "slice of water 2m high,at the bottom of the lock.As a rule ,if the horizontal area of the lock chamber is A and the elevation difference is H,we must fill the lock with the volume AH of water each time boats are passing through the lock,irrespective of how many there are,or how big.

The lock is belmont on the grand canal.

im invisible

fergal.b wrote: »

What if one of the boats is a half submerged submarine.:D

or how about, a half submerged submarine, untill the lock is closed behind it, then it fully submerges, raising the water level by whatever...