zaro

What is the formula for the buoyant force of a submerged object?

Published in Fluid Mechanics 3 mins read

The exact formula for the buoyant force ($F_B$) of a submerged object is:

$F_B = \rho g V$

This formula is derived from Archimedes' Principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

How to Calculate Buoyant Force

To apply this formula correctly and determine the buoyant force on an object, follow these key steps:

Step 1: Determine the Volume of the Submerged Object and Fluid Density

Before calculating the force, you must first identify the essential physical properties:

  1. Volume of the Submerged Object ($V$): Determine the exact volume of the object that is submerged within the fluid. If the object is fully immersed, this will be its total volume. If it is only partially submerged (e.g., a floating boat), it is only the portion of the object's volume that is below the fluid's surface.
  2. Density of the Fluid ($\rho$): Identify the density of the fluid in which the object is submerged. It's crucial to use the density of the fluid (e.g., water, oil, air), not the density of the object itself.

Step 2: Apply Archimedes' Principle Using the Formula

Once you have the values for the submerged volume and the fluid's density, you can use the formula $F_B = \rho g V$.

Here's a breakdown of each component in the buoyant force formula:

Variable Description Standard SI Unit (for calculation)
$F_B$ Buoyant Force (the upward force exerted by the fluid) Newtons (N)
$\rho$ Density of the Fluid (rho) Kilograms per cubic meter (kg/m³)
$g$ Acceleration due to Gravity (a constant value) Meters per second squared (m/s²)
$V$ Volume of the Submerged Part of the Object Cubic meters (m³)

Note on $g$: The value of 'g' (acceleration due to gravity) is approximately 9.81 m/s² on Earth, but it can be rounded to 9.8 m/s² or 10 m/s² for simpler calculations depending on the required precision.

Practical Applications of Buoyant Force

Understanding the buoyant force is fundamental in various fields, from engineering to everyday observations:

  • Floating and Sinking: The buoyant force dictates whether an object will float or sink. If the buoyant force acting on an object is greater than or equal to its weight, the object will float. If the object's weight is greater than the buoyant force, it will sink.
  • Ship Design: Naval architects meticulously calculate buoyant forces to ensure that ships can carry heavy cargo without sinking. A ship's hollow hull displaces a large volume of water, generating a significant buoyant force that counteracts its weight.
  • Submarines and Hot Air Balloons: These technologies precisely manipulate buoyancy. Submarines use ballast tanks to take in or expel water, changing their effective density to ascend or descend. Hot air balloons use heated air, which is less dense than the surrounding cooler air, to generate lift via buoyancy.

By accurately applying the formula $F_B = \rho g V$, one can predict and control the behavior of objects in fluids, crucial for diverse applications and scientific understanding.