We saw in Chapter 3 that the buoyant force, FB, on a body...

We saw in Chapter 3 that the buoyant force, $F_{B},$ on a body submerged in a fluid is directly proportional to the specific weight of the fluid, $\gamma$. Demonstrate this using dimensional analysis, by starting with the buoyant force as a function of the volume of the body and the specific weight of the fluid.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Dimensional Analysis

A technique used in physics and engineering to check relationships by comparing the dimensions (units) on both sides of an equation. It helps verify that derived formulas are consistent and can also reveal underlying proportionality relationships between physical quantities.

Buoyant Force

The net upward force exerted on an object immersed in a fluid, which counteracts the object's weight. This force is central to understanding flotation and is determined by the volume of fluid displaced and the fluid's specific weight.

Specific Weight

The weight per unit volume of a substance, typically a fluid. It quantifies how much force a fluid exerts due to gravity on a given volume, playing a crucial role in determining the magnitude of buoyant forces.

Volume

The measure of space occupied by an object or the fluid displaced by the object. In buoyancy calculations, the volume of the displaced fluid directly influences the buoyant force experienced by the object.

Direct Proportionality

A relationship where one quantity increases or decreases in direct correspondence with another, such that their ratio remains constant. In the context of buoyancy, the buoyant force is directly proportional to both the fluid's specific weight and the volume of the displaced fluid.

Please give Ace some feedback