Archimedes’ principle in fluid mechanics — when a body is fully or partially immersed in a fluid, the buoyant (upthrust) force acting on it is equal to which quantity?

Introduction / Context:
Archimedes’ principle is a foundational concept in fluid mechanics and naval architecture. It explains why objects float or sink in liquids and gases and quantifies the upward buoyant force that a fluid exerts on an immersed body. Understanding this principle is essential for designing ships, hydrometers, and many process equipment items such as separators and level instruments.

Given Data / Assumptions:

• The body may be totally or partially immersed in a static fluid.
• The fluid is continuous and at rest (hydrostatics).
• Pressure increases with depth according to p = p0 + rho * g * h.
• Gravity acts uniformly with acceleration g.

Concept / Approach:

The buoyant force arises from the hydrostatic pressure distribution on the body’s surface. Pressure is higher at deeper points, producing a net upward resultant. Mathematically, integrating the pressure over the wetted surface is equivalent to the weight of the displaced fluid volume. Therefore, the magnitude of upthrust depends only on the displaced fluid, not directly on the body’s own weight.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

A force balance on a floating body at equilibrium gives upthrust = weight. Measuring displaced fluid (e.g., via overflow) directly confirms buoyant force equals the displaced fluid’s weight.

Why Other Options Are Wrong:

“Weight of the body” confuses buoyancy with gravity; “weight of the body and fluid displaced” double counts; “difference of weights …” is not the definition of buoyancy (though net force uses a difference); “none” contradicts Archimedes’ principle.

Common Pitfalls (misconceptions, mistakes):

Assuming buoyant force depends on the body’s density directly; forgetting that compressible fluids (gases) also exert buoyancy; neglecting that partial immersion displaces less fluid and thus reduces upthrust.

Final Answer:

weight of the fluid displaced by the body