A pressure difference produces upthrust
Definition
Upthrust
The resultant upward force that a fluid exerts on an object within it.
- Fluid pressure acts normal to every surface of an immersed object.
- Because pressure increases with depth, the upward force on the lower surface is greater than the downward force on the upper surface.
- The resultant of the fluid-pressure forces is an upward force called upthrust.
- Sideways pressure forces cancel for a symmetrical object in a stationary fluid.
Upthrust equals displaced-fluid weight
- The magnitude of upthrust equals the weight of fluid displaced by the immersed part of the object.
- For fluid density ρ\rhoρ, displaced volume VVV and gravitational field strength ggg, this can be written as U=ρVgU=\rho VgU=ρVg.
- A fully immersed object with fixed volume displaces the same volume wherever it is in an incompressible liquid, so its upthrust is unchanged with depth.
- A partially immersed object displaces only the volume below the surface.
Example
Finding upthrust
- An object displaces 2.5×10−3 m32.5\times10^{-3}\,\text{m}^32.5×10−3m3 of water with ρ=1000 kg m−3\rho=1000\,\text{kg m}^{-3}ρ=1000kg m−3 and g=10 N kg−1g=10\,\text{N kg}^{-1}g=10N kg−1.
- U=ρVg=1000×2.5×10−3×10=25 NU=\rho Vg=1000\times2.5\times10^{-3}\times10=25\,\text{N}U=ρVg=1000×2.5×10−3×10=25N.
Gases also provide upthrust
- A balloon displaces air, so the surrounding air exerts upthrust equal to the weight of the displaced air.
- Upthrust increases when more fluid is displaced or when the fluid is denser.
Common Mistake
Do not state that upthrust is caused simply by water pushing upwards; explain the pressure difference between the lower and upper surfaces.
Self review
- Why is the pressure force larger on the bottom of an immersed object?
- What is upthrust equal to?
- How can upthrust be calculated from displaced volume?
- Why can a balloon experience upthrust in air?
