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It seems intuitive that a (waterproofed) spring-based scale placed at the bottom of a lake would indicate the weight of the water column above it.

But assume the scale sinks from the surface of the lake to the bottom, while staying parallel to the bottom at all times. Would the scale still indicate the weight of the water column at that moment, while it's falling, before it lands on the bottom?

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You can see a water-sealed spring-based scale as a pressure gauge. Its indication will therefore be connected to the hydrostatic pressure:

$$P=\rho g h$$

where $\rho$ is the water density, $g$ is the gravitational acceleration and $h$ is the depth.

Now, if the scale has a surface of A, it will indicate a force of:

$$F=PA=\rho g h A=\rho g V =g M$$

where $M$ is the mass of the column of water above the scale with base area equal to $A$.

Also note that the force measured by the scale does not depend on its orientation (it doesn't have to be parallel to the bottom), as the pressure is a scalar quantity.

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  • $\begingroup$ "Connected to" the pressure, yes. But how? $\endgroup$
    – Emilio Pisanty
    Commented Jun 4, 2017 at 12:37
  • $\begingroup$ @EmilioPisanty I thought that the how was trivial. I added it anyway ;) $\endgroup$
    – DarioP
    Commented Jun 5, 2017 at 9:32

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