Physics

# The Physics Philes, lesson 89: Sink or Swim

OK, class. Let’s talk a little more about fluid mechanics.

You’re probably already pretty familiar with buoyancy. It’s why you float in water and why helium balloons float in the air. Those things are just a physical manifestation of something called Archimedes’s Principle:

When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

To illustrate this, let’s think about a fluid element within a fluid, and all of the fluid is at rest. It might look a bit like this:

That dotted line irregular shape is the outline of our fluid element. When the entire fluid in equilibrium, the sum of all the y-components of force on the fluid must be zero. In addition, the sum of the y-components of the surface forces must be an upward force equal to the magnitude of the weight of the fluid inside the surface. In addition to that, all the torques on the fluid element must be zero, as well, resulting in a y-component of surface force that must past through the fluid element’s center of gravity.

No, replace that fluid element with a solid of the same shape and size. The pressure at every point is the same as before. The total upward force the fluid exerts on the solid is the same. This force has a name; it’s called the buoyant force. When the density of an object is less than the density of the fluid it’s in, it will float. Hence, you float in water and a helium balloon will float in the air.

So the buoyant force allows you to float in water, but you’re still in the water. There are some thing, like paper clips, that have a higher density than water, but nevertheless can be folding in such a way that it will kind of just sit on the top of water. What’s up with that? Surface tension, that’s what up with that.

Surface tension is what happens when a liquid behaves like a membrane under tension. The liquid molecules exert an attractive force on each other. Those forces inside the liquid equal zero, but on the surface the molecules are actually pulled toward the inside of the volume. As such, liquids tend to try to minimize surface area.

This is really important on a microscopic level, but not so much on the macro scale. Surface tension explains why raindrops are round (a sphere has a pretty big surface area to volume ratio). The effect of surface tension is very large for the very small. But don’t try running across the water. The effect of surface tension is very small and you’ll look something like this:

That’s all for now. Come back next week for more fluid mechanics!

Featured image credit: felixtsao