Physics help, buoyancy?

Question

Imagine a canal that includes a tunnel so that people can drive under the canal. The canal connects two lakes. A boat in one lake crosses the tunnel to the other lake. Does the force on the tunnel increase when the boat is on the canal? Thanks.

Answer 1

No. When things float they displace their own weight in water.

Answer 2

No.  The force on the tunnel is determined by the water pressure, which is determined entirely by the depth of the tunnel under the water's surface (regardless of what's floating on top).  Since the the surface level doesn't change when the boat goes from lake to canal, the water pressure on the tunnel doesn't change.

Interestingly, though, the force on the tunnel DOES change when the boat first gets into the lake!  That's because the boat causes the lake & canal's water level to raise very slightly (a tiny fraction of an inch), resulting in a very slight increase in water pressure at the depth of the tunnel.