413 Upthrust

  • When a foreign object is submerged in a fluid, the surrounding fluid will exert pressure forces perpendicularly into each point on the surface of the foreign object.
  • Because pressure increases with depth, the resultant of these pressure forces is an vertically upward force. This force is called the force of upthrust, U.


  • With some simple reasoning, we can deduce that the magnitude of the upthrust must be equal to the weight of the displaced fluid. Hence

U={{m}_{f}}g={{\rho }_{f}}{{V}_{f}}g

  • To generate a larger upthrust, a body must displace more fluid.
  • Similar to weight, upthrust appears to act at a single point, the centre of gravity of the displaced fluid.


  • Compare the upthrust U

U={{m}_{f}}g={{\rho }_{f}}{{V}_{f}}g

  • with the weight of the object W

W={{m}_{o}}g={{\rho }_{o}}{{V}_{o}}g

  • When an object is fully submerged, Vf = Vo. This also represents the maximum upthrust the object can generate.



  • If ρo > ρf , then W > Umax.
    • The object will sink.
  • If ρo = ρf, then W = Umax.
    • The object will neither sink nor float.
    • It can hover at equilibrium at any depth in the fluid as long as it is fully submerged.
  • If ρo < ρf, then W < Umax.
    • The object will float partially submerged.
    • It will displace just enough fluid to generate the amount of upthrust exactly equal to its weight.
    • The lower the object’s density, the higher it will float.



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