It should be noted, though, that changes in liquid density will have absolutely no effect on
hydrostatic measurement of liquid mass, so long as the vessel has a constant cross-sectional area
throughout its entire height. A simple thought experiment proves this: imagine a vessel partially
full of liquid, with a pressure transmitter attached to the bottom to measure hydrostatic pressure.
Now imagine the temperature of that liquid increasing, such that its volume expands and has a
lower density than before. Assuming no addition or loss of liquid to or from the vessel, any increase
in liquid level will be strictly due to volume expansion (density decrease). Liquid level inside this
vessel will rise, but the transmitter will sense the exact same hydrostatic pressure as before, since
the rise in level is precisely countered by the decrease in density (if h increases by the same factor