Buoyancy
Buoyancy is the upward force exerted by a fluid on an object submerged or partially submerged in it, opposing the weight of the object. This force arises because fluid pressure increases with depth, so the pressure on the bottom face of a submerged object is greater than on the top face, creating a net upward force. An object floats when the buoyant force equals its weight, and sinks when its weight exceeds the buoyant force.
Key Formula
Fb = ρ_fluid × V_submerged × g
LaTeX: F_b = \rho_{\text{fluid}} \cdot V_{\text{sub}} \cdot g
| Symbol | Meaning | Unit |
|---|---|---|
| F_b | Buoyant force | N |
| \rho_{\text{fluid}} | Density of the fluid | kg/m³ |
| V_{\text{sub}} | Volume of fluid displaced (submerged volume) | m³ |
| g | Acceleration due to gravity | m/s² |
Worked Example
Problem
A block of wood with volume 0.020 m³ and density 600 kg/m³ is placed in water (ρ = 1000 kg/m³). Find the buoyant force and the fraction of the block that floats above the surface.
Solution
Step 1: Weight of block — W = ρ_wood × V × g = 600 × 0.020 × 9.8 = 117.6 N. Step 2: For floating, Fb = W, so ρ_water × V_sub × g = 117.6. Step 3: V_sub = 117.6 / (1000 × 9.8) = 0.012 m³. Step 4: Fraction submerged = 0.012/0.020 = 0.60 (60%). Step 5: Fraction above water = 1 − 0.60 = 0.40 (40%).
Answer
Buoyant force = 117.6 N; 60% of the block is submerged; 40% floats above water.
Buoyant force on a 1 L (0.001 m³) object fully submerged in various fluids
| Fluid | Density (kg/m³) | Buoyant Force (N) | Will Steel Sink? | Application |
|---|---|---|---|---|
| Air (at sea level) | 1.225 | 0.012 | Yes | Hot-air balloons |
| Fresh water | 1000 | 9.81 | Yes | Swimming pools |
| Sea water | 1025 | 10.05 | Yes | Ships, submarines |
| Glycerol | 1261 | 12.37 | Yes (mostly) | Lab density tests |
| Mercury | 13,546 | 132.9 | No (floats) | Barometers |
Interactive Tools
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Related Terms
Archimedes' Principle
Archimedes' Principle states that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This principle was discovered by Archimedes of Syracuse around 246 BCE, reportedly while stepping into a bath and observing water overflow. It is fundamental to naval architecture, submarine design, hot-air balloon operation, and density measurement techniques.
Pascal's Law
Pascal's Law states that pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions throughout the fluid and acts with equal force per unit area on all surfaces of the container. Formulated by Blaise Pascal in 1653, this principle is the foundation of hydraulic systems used in hydraulic lifts, car brakes, excavator arms, and hydraulic jacks. The law assumes the fluid is incompressible and at rest (hydrostatic conditions).
Fluid Pressure
Fluid pressure is the force exerted per unit area by a fluid on any surface in contact with it, arising from the continuous collisions of fluid molecules. In a static fluid, pressure at a given depth depends on the fluid's density, gravitational acceleration, and the depth below the free surface. It is fundamental to hydraulics, hydrostatics, and the design of dams, pipelines, and pressure vessels.
From Spanish "boyante" (buoyant, floating), derived from "boya" (buoy), which traces back to Old French "boie" or Dutch "boei" (fetter, buoy). The scientific understanding was established by Archimedes of Syracuse around 246 BCE.