Upthrust: The Invisible Force That Makes Things Float
The Discovery and Principle of Buoyancy
The story of upthrust begins over 2000 years ago with the ancient Greek scientist Archimedes. Legend says the king suspected his new crown was not made of pure gold. He asked Archimedes to find out without damaging the crown. While taking a bath, Archimedes noticed that the water level rose as he got in. He realized that the amount of water displaced was equal to the volume of his submerged body. Excited by this discovery, he reportedly ran through the streets shouting "Eureka!" (I have found it!).
This led to the formal statement known as Archimedes' Principle:
This principle applies to all fluids, meaning both liquids (like water and oil) and gases (like air). The force itself is what we call upthrust or buoyant force. For example, when you push an empty plastic bottle underwater, you can feel this upward push trying to bring it back to the surface. That feeling is the upthrust in action.
Why Does Upthrust Happen? The Science of Pressure
Upthrust isn't magic; it's a result of the pressure exerted by a fluid. Pressure is defined as force per unit area ($Pressure = Force / Area$). In a fluid, pressure increases with depth. The deeper you go, the greater the weight of the fluid above you, and thus the higher the pressure.
Imagine submerging a cube in water. The water pressure on the bottom surface of the cube is greater than the pressure on its top surface because the bottom is at a greater depth. This difference in pressure creates a net upward force. This net force is the upthrust.
We can express the magnitude of the upthrust ($F_b$) with a simple formula derived from Archimedes' principle:
Where:
$F_b$ = Buoyant Force (Upthrust) in Newtons (N)
$\rho_{fluid}$ = Density of the fluid in kilograms per cubic meter (kg/m³)
$V_{displaced}$ = Volume of fluid displaced by the object in cubic meters (m³)
$g$ = Acceleration due to gravity (9.8 m/s²)
Notice that the upthrust depends on the density of the fluid and the volume of the object submerged, but not on the object's own density or what it's made of (though that determines how much of it submerges). A small piece of steel sinks, but a giant steel ship floats because the ship displaces a huge volume of water, creating a massive upthrust.
Sink, Float, or Hover? The Role of Density
The fate of an object in a fluid—whether it sinks, floats, or remains neutrally buoyant (hovering)—is decided by the battle between two forces: the object's weight ($W_{object}$) pulling it down, and the upthrust ($F_b$) pushing it up. The key factor that determines the outcome is density. Density ($\rho$) is mass per unit volume ($\rho = m / V$).
Let's compare the density of the object ($\rho_{object}$) with the density of the fluid ($\rho_{fluid}$):
| Condition | Forces | Result | Example |
|---|---|---|---|
| $\rho_{object} > \rho_{fluid}$ | Weight > Upthrust ($W > F_b$) | Object Sinks | A stone in water |
| $\rho_{object} = \rho_{fluid}$ | Weight = Upthrust ($W = F_b$) | Object Hovers (Neutral Buoyancy) | A submarine at a constant depth |
| $\rho_{object} < \rho_{fluid}$ | Weight < Upthrust ($W < F_b$) | Object Floats | An ice cube in water, a ship |
For a floating object, the upthrust is exactly equal to its weight. The object will sink into the fluid until it displaces a volume of fluid whose weight equals its own.
Upthrust in Action: From Ships to the Sky
The principles of upthrust are not just theoretical; they are essential to countless technologies and natural phenomena.
Shipbuilding: A solid block of iron sinks because its density is much higher than water. However, a ship made of the same iron floats. Engineers shape the ship into a hollow structure. This hollow shape encloses a large volume of air, which has very low density. The average density of the ship (the total mass of the ship and its cargo divided by its total volume) becomes less than the density of water. This is why massive cargo ships can carry heavy loads across the oceans.
Submarines: Submarines are marvels of buoyancy control. They have special tanks called ballast tanks. To dive, the submarine fills these tanks with water, increasing its average density until it becomes greater than the surrounding water. To surface, it pumps compressed air into the tanks, forcing the water out. This decreases the average density, making the submarine rise. To hover, it adjusts the water and air to achieve neutral buoyancy.
Hot Air and Helium Balloons: Upthrust works in gases too! Air has density. A balloon filled with hot air or helium has a lower average density than the surrounding cooler air. The cooler, denser air around the balloon exerts an upthrust greater than the weight of the balloon, causing it to rise. A hot air balloonist controls altitude by heating the air inside the balloon (to rise) or letting it cool (to descend).
Swimming and Life Jackets: The human body is slightly less dense than water when the lungs are full of air, making it possible to float. Life jackets are filled with lightweight, porous materials that increase the wearer's volume without adding much weight, significantly increasing the upthrust and ensuring buoyancy even for non-swimmers.
Hydrometers: This is a scientific instrument used to measure the density of a liquid. It is a sealed glass tube with a weighted bottom. It floats upright in the liquid. The depth to which it sinks indicates the liquid's density—the denser the liquid, the higher the hydrometer floats (less of it is submerged to displace an equal weight of liquid).
Common Mistakes and Important Questions
Indirectly, yes. The upthrust exists because of the pressure difference in the fluid, which is caused by the weight of the fluid itself. In a zero-gravity environment (like in orbit), there is no buoyancy because fluids do not have weight, and thus no pressure gradient exists to create upthrust.
No, not directly. The magnitude of the upthrust depends only on the density of the fluid and the volume of the object that is submerged ($F_b = \rho_{fluid} V_{displaced} g$). A 1 kg sphere of steel and a 1 kg sheet of steel will experience the same upthrust if fully submerged because they displace the same volume of water. However, shape is critical for stability (e.g., a flat-bottomed boat is more stable than a round one) and for determining whether the object will sink or float (a sheet of steel might float if it can displace enough water without submerging completely).
When the rock is submerged, the water exerts an upthrust on it. This upthrust counteracts some of the rock's weight. The force you need to apply to lift it is the rock's weight minus the upthrust. On land, you have to overcome the full weight of the rock. This is why objects feel lighter when they are in water.
Footnote
1 Buoyant Force: Another term for upthrust; the upward force exerted by a fluid on an immersed object.
2 Archimedes' Principle: The physical law stating that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid the body displaces.
3 Density ($\rho$): A measure of mass per unit volume, typically expressed in kilograms per cubic meter (kg/m³) or grams per cubic centimeter (g/cm³).
4 Fluid Displacement: The volume of fluid that is pushed aside when an object is placed in it. This volume is equal to the volume of the part of the object that is submerged.
5 Neutral Buoyancy: The state where an object's average density is equal to the density of the surrounding fluid, causing it to neither sink nor float but to remain suspended.