Fluids: Liquids and Gases

Pressure in Liquids

Floating Mountains


Image: Modified from NatureObjects float with a portion of their mass below the surface and the rest sticking up out of the liquid.  The amount of a floating mass under the surface simply equals the density of the mass divided by the density of the liquid. For icebergs the density of ice is 917 kg/m3 and the density of seawater is 1025 kg/m3, so that 917/1025 = 89% of the volume of the iceberg is below the water level.


For white pine wood the density is 373 kg/m3, and if a log of it rolls into a fresh water lake (density = 1000 kg/m3) the fraction below the lake level is 37% - most of it floats above the surface. Of course, the longer the log floats in the lake the more water will soak into the porous wood, causing the log to become denser, sinking lower into the lake.


There are much bigger things than icebergs that float. The entire crust of the Earth is relatively brittle material that floats on a slowly flowing mantle. The mantle is a fluid, but one with very high viscosity or resistance to flow. Plate tectonics exists because over time the crust and upper mantle are carried by the underlying flowing mantle. The movement is a few centimeters per year. Earth's crust moves about the same rate as your fingernails grow. At the same time it is moving horizontally the continental crust floats in the mantle. The density of the crust varies from place to place but averages about 85% of the mantle’s density. That means that for a tall feature like 8.8 km high Mount Everest, the observed height is just 15% of the entire thickness of the mountain, so a root about 50 km deep must extend below the ground level. (Actually, the root under Everest is about 75 km thick because the crust is nearly doubled in thickness there). Because mountains float, as erosion lowers their summits, they buoyantly rise. Thus, the continuing existence of the 200 million year old Appalachian Mountains demonstrates that uplift is still occurring and will continue until the root is reduced to the normal crustal thickness. Mountain ranges that are built in a few tens of millions of years can last for a billion years.


There is something even bigger than mountains that could float. The giant ringed planet Saturn is made up mostly of gases and has a density of 687 kg/m3, much less than the density of water. If there were a big enough ocean, Saturn would float. Isn’t physics fun?


Image: www.conceptvisions.net84.net

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