Tiltmeter Problem: Calculating Water Level Changes in Geologic Measurements

[bcjochim07]

Homework Statement

Geologists place tiltmeters on the sides of volcanoes to measure the displacement of the surface as magma moves inside the volcano. Traditional tiltmeters consist of two or more water filled metal cans placed some distance apart and connected by a hose. Suppose two can are placed so that the water level in both is initially at the 5 cm mark. A week later, the water level in can 2 is at the 6.5 cm mark. The cans are 100 m apart.

a) Did can 2 move up or down relative to can 1? By what distance?

b) Where is the water level now in can 1?

Homework Equations

The Attempt at a Solution

For part a, here is what I thought, but I'm not sure that it's right:

Since the water in can 2 rises, the pressure increases. I think that the pressure in both of the cans has to be the same. Since can 1 now has a lower water level, it must be at a lower level than can 2. Does can 2 move up by 1.5 cm?

 

[mgb_phys]

It's simpler than that.
The water level in each stays the same - relative to the mountain.
Just draw a diagram, draw a straight line across the paper to represent the water level then try and draw a tilted pair of cans to see how the level relative to the cans would change,

 

[bcjochim07]

Ok, I tried that, but I don't think I understand the underlying concept. Is this a pressure problem?

 

[mgb_phys]

Only indirectly.
The water level in the two cups remains the same ( relative to earth)
If the water level 'appears' to drop 1cm in one cup it means that the cup has moved 1 cm up - the water level is really staying the same.