Search results for: “density”

Reader Question: Hot Air Balloon Physics
lazenby asks:
and boyancy in air? is the lifting capacity of a hot air balloon equal to the modulo of the weight of the air in the balloon with the weight of the same volume of air outside the balloon?
for that matter, does the lift of a big helium weather balloon decrease as air pressure, and so weight of the air outside the balloon, drops? and is this exactly counterbalanced by the lessening density of the helium in the balloon?
all of these things keep me awake.
Hopefully you won’t be sleepless much longer. Buoyancy in air follows the same principles as buoyancy in water. Determining the lifting capacity of a balloon is a matter of determining how heavy the balloon can be before the buoyant force is equal to the weight. See the free body diagram and little derivation below to see what the maximum payload mass is for a helium balloon. You can click on the picture to enlarge it.
The second part of your question raises some interesting points. As a balloon’s altitude increases, the atmosphere around it gets colder and less dense, all of which should reduce the buoyant force. At the same time, the balloon itself expands to equalize the pressure inside and outside of the balloon, which should increase the buoyant force. (At some point the pressure drops sufficiently that the tensile strength of the balloon material is unable to cope with that expansion and the balloon bursts, but we’ll ignore that here.) For this problem, we’d want to know what payload the balloon can carry without losing lift, and, with a couple assumptions, that’s pretty easy to figure out. I’ve done that derivation below.
The real key to the calculation is assuming that the helium in the balloon maintains the same temperature as the air outside. Since balloons rise slowly, this seemed a more reasonable assumption than imagining that the balloon remains warm compared to its surroundings. That calculation is doable as well but requires more than a couple lines, unfortunately! Thanks for your questions!
January 13, 2011
Reader Question: Swimming and Buoyancy
aniiika asks:
How does buoyancy relate to swimming?
Buoyancy is the force that enables a swimmer to float in the water, even when still. Buoyant force is equal to the weight of the fluid displaced by the swimmer; in other words, the density of the fluid multiplied by the volume of the swimmer that is submerged.
Different people float at different heights in the water depending on many factors, such as body shape, amount of fat, and how much air is in their lungs. All of these things affect a person’s volume and/or density, thereby affecting the buoyant force they experience.
Because a person’s body is not fully submerged their center of buoyancy–the point where all buoyant forces on the body can be represented by a single force–does not coincide with the center of mass (sometimes referred to as center of gravity). Where those forces are relative to one another determines the stability of a person floating in the water. Everyone’s center of buoyancy is higher than their center of mass, so people always float stably in an upright orientation. Our legs, for example, don’t float as well as our torsos, so, when floating horizontally, one’s legs will tend to sink.
Swimmers can control their buoyancy to their advantage by actually pressing their upper chests further into the water. This tends to bring one’s hips closer to the surface and can reduce drag (#).
January 11, 2011
Thermal Convection
This video turbulent convection in a vertical channel. Buoyancy and the density variations caused by small differences in temperature are what drive the behavior.
December 23, 2010
Oil Chandeliers
What you see above is a composite of images of an oil droplet falling into alcohol from two different heights. The top row of images is from a height of 25 mm and the bottom from a height of 50 mm. The first droplet forms an expanding vortex ring which breaks down via the Rayleigh-Taylor instability due to its greater density than the surrounding alcohol. The second droplet impacts the alcohol with greater momentum and is initially deformed by viscous shear forces. Eventually it, too, breaks down by the Rayleigh-Taylor mechanism. This image is part of the 2010 Gallery of Fluid Motion. # (PDF)
November 19, 2010
Seeing Shock Waves with Schlieren
Schlieren photography is actually a pretty commonly used system in high-speed experimental aerodynamics. A typical schlieren system will shine a collimated light source on the target (a wind tunnel test section or, above, a candle), bounce that light off a mirror, block half the light with a knife-edge at the focal point, and then record the subsequent images with a camera (high-speed or otherwise). The density of air is closely related to its index of refraction, so light that hits air of a different density will be bent more or less than a neighboring ray. This uneven bending of the light rays due to density gradients is what causes the light and dark areas on the schlieren images. Since the density of air changes drastically across a shock wave, the schlieren system is perfect for visualizing shock waves and has, in fact, been used for that purpose since 1864!
October 19, 2010
Convection in Cream and Liqueur
We are used to associating convection with differences in temperature, but what’s actually necessary for a Rayleigh-Taylor-type instability is a density variation (and a gravitational field). The solutal convection seen above when mixing liqueur with cream is caused by the interaction of density and surface tension. When the alcohol of the liqueur mixes with the cream, it forms a less dense alcohol-cream that tries to rise to the surface. The alcohol also breaks the surface tension of the cream, causing it to contract and open cells where the alcohol surfaces. As the alcohol evaporates, the alcohol-cream mixture gets denser and sinks back down where it can pick up more alcohol and start the process again. (via jshoer and io9)
October 18, 2010
The Sound of Helium
Gases of different density are good for more than just physics demonstrations. They also affect the transmission of sound waves, thereby altering our perception of pitch. As fun as sulfur hexafluoride is, though, don’t go playing with it at home; it’s an extremely potent greenhouse gas.
August 18, 2010
Shock Waves From a Gun
Often fluid motion is invisible to the human eye. Researchers use techniques like schlieren photography to make changes in fluid density apparent. In this high-speed schlieren photo, an AK-47 is being fired. The spherical shock wave centered on the gun’s muzzle is due to the explosive discharge of gases used to fire the bullet. At the left of the frame, the bullet also causes a shock wave, this time a conical one, as it travels supersonically out of the gun.
Photo Source; Credit: Gary Settles, Penn State Gas Dynamics Lab
July 28, 2010

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