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Gravity pushes flames and hot air up

Q: I am an 8-year-old boy and I want to know how and why fire travels upwards. (Ben, Kittredge, Colorado)

Q: Why does a candle flame defy gravity? (Retnawati, Singapore)

A: A flame goes up because the denser surrounding air pushes it up.

Fire bobs up through surrounding denser air much as a cork rises to the water surface — pushed by greater pressure from denser air below. [Photo Credit:US Fish and Wildlife Service]

A flame consists of gases so hot they glow yellow, orange, and red. Hot gasses expand and become less dense than the surrounding air. Therefore, the flame is lighter than an equal volume of air.

A flame goes up much as a submerged cork bobs to the water surface when released. The flame is lighter than air and the air’s buoyant force is, therefore, strong enough to push the flame up.

Actually, the flame doesn’t defy gravity but rather the flame goes up because of gravity. Gravity causes buoyancy.

Buoyant force. In the third century BC, Archimedes discovered the buoyant force when he settled into a bath of water, legend has it, and felt lighter as his body displaced the bath water. We’ve encountered the same lightness as we wade into a swimming pool. We can even float, sustained by the water’s buoyant push.

Archimedes’ principle applies to air as well as water: a force equal to the weight of the air displaced buoys up an object surrounded by air.

We scarcely think of air at all. It’s so nebulous and pervasive. But our atmosphere has considerable mass because it towers at least 50 miles (80 km) above Earth’s surface into space. Air provides a buoyant push just as water does. A column of air that extends from sea level to space with a tiny postage-stamp size cross sectional area — one square inch — weighs almost 15 pounds and, consequently, exerts a pressure of 15 pounds per square inch on the bottom of the column.

Pressure decreases with altitude because the air column to space is shorter, contains less air and, thus, weighs less. The pressure on top of Mount Everest, for example, (5.5 miles [8.7 km] high) is only about 5 pounds per square inch because Everest pokes two-thirds the way up through our troposphere (the cloud-forming atmosphere up to 10 miles [16 km]). There’s not much air above the mountain to press down on it.

Imagine an air parcel immersed in the ocean of air that is our atmosphere. See figure. The surrounding air presses in on the air parcel from all directions but the pressure along the sides of the parcel are equal and opposite and thus cancel.

The pressure on the top of the parcel is less than the pressure at the bottom (since pressure decreases with altitude). That pressure difference is the buoyant force — the force that pushes up on the air parcel.

Pressure along the sides of the air parcel cancel. The pressure on the bottom is greater than on top. The difference (Bottom - Top) is the buoyant force that pushes up on the air parcel.

The air parcel, however, has mass and therefore weight. Gravity pulls it down. If gravity’s pull is less than the buoyant upward push, the parcel rises. If gravity’s pull is greater than the buoyant push, it falls.

If the parcel contains light hot air from a flame, then gravity’s pull is less than the buoyant push. That’s why fire goes up.

A candle burning in free fall where there is no “up.” [NASA]

By the way, a spacecraft orbiting Earth is in free fall as are all objects inside the craft. So, no "down" force holds objects to the bottom of the craft or provides buoyancy. We might suspect that flames in space act funny. Right! The flame does not go up. The flame’s hot gasses expand as a sphere about a candle’s wick, forming a fireball.

Further Reading:

Hyperphysics by Rod Nave: Buoyancy

Scientific American: How does a flame behave in zero gravity by Kenneth Schlecht

Hewitt, Paul G. Conceptual Physics. New York: Addison-Wesley, 1998.

Williams, Jack. The Weather Book. New York: Vintage Books, 1997.

Q: I occasionally see references to "hot air rising" causing cooler air to rush in to replace it. Can hot air actually rise by itself or is it only pushed up from below by denser air? (Lanney, Sandia Park, New Mexico)

A: Hot air has no "strange tendency" to rise says physicist Paul G. Hewitt in his Conceptual Physics.

Hot air rises because it is light enough (that is, lighter than the surrounding air) that gravity’s pull is less than the buoyant push.

The air below exerts greater pressure on the hot air than the air above. This pressure difference provides a buoyant force great enough to lift the lighter hot air.

(Answered Feb. 18, 2005)