Buoyant Force

Unit 2 Displacement

Buoyant Force

Juan Juan
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Buoyant Force is the upward, directed force exerted by a fluid on an immersed body, arising from the pressure difference between the bottom and top of the object. It is the Mid Displacement force in Superphysics’ Liquid Relationalities — the linear, translational action of the liquid medium as it redistributes itself around a displaced body through aetherspace and the outer intraaetherspace.

Unlike cohesive adhesive (rotational/cohesive), buoyant force is directional and linear — fluid pushes upward along a straight line to restore equilibrium.

The Equation: Buoyancy Fundamentals

Archimedes’ Principle (Displacement Law)

Fb=ρfgVd F_b = \rho_f g V_d

Where:

Symbol Meaning Unit
Fb F_b Buoyant force (upward) N \text{N}
ρf \rho_f Fluid density kg/m3 \text{kg}/\text{m}^3
g Gravitational acceleration m/s2 \text{m}/\text{s}^2
Vd V_d Displaced fluid volume m3 \text{m}^3

Pressure Gradient Origin (Micro Displacement)

Fb=∮SP dA=−ρfgVd z^ F_b = \oint_{\mathcal{S}} P \, d\mathbf{A} = -\rho_f g V_d \, \hat{\mathbf{z}}

Where:

Symbol Meaning Unit
∮S \oint_{\mathcal{S}} Surface integral over the body —
P Hydrostatic pressure at depth Pa \text{Pa}
dA d\mathbf{A} Outward area element m2 \text{m}^2
z^ \hat{\mathbf{z}} Vertical unit vector (upward) —

Hydrostatic Pressure Difference (Displacement Driver)

ΔP=ρfgh \Delta P = \rho_f g h

Where h is the depth difference between the bottom and top of the immersed body. The larger pressure at the bottom pushes upward — pure linear displacement.

Floating Condition (Equilibrium)

ρfVd=ρbVb \rho_f V_d = \rho_b V_b

Where ( \rho_b ) is body density and ( V_b ) is total body volume. The fraction submerged is:

VdVb=ρbρf \frac{V_d}{V_b} = \frac{\rho_b}{\rho_f}

Key Properties of Buoyant Force

Property Explanation
Directional Always acts vertically upward
Linear Pushes along a straight line opposing gravity
Volume-dependent Depends on displaced fluid volume, not body mass
Density-dependent Heavier fluids produce greater buoyancy
Depth-independent Net buoyancy same at any depth (for incompressible fluid)
Pressure-driven Arises from pressure gradient across body height
Restoring Returns floating bodies to equilibrium position

Stability Condition (Metacenter)

GM=IVd−BG GM = \frac{I}{V_d} - BG

Where

GM GM

is metacentric height, I is moment of inertia of waterplane, and ( BG ) is center-of-gravity to center-of-buoyancy distance. Stable if GM > 0.

Real-Life Examples

Example How Buoyant Force Works
1. Ships floating Hull displaces water; buoyancy balances ship’s weight
2. Submarines diving Ballast tanks fill with water, reducing buoyancy
3. Hot air balloons Heated air is less dense; displaced cool air pushes balloon up
4. Icebergs ~90% submerged because ice density is ~90% of water
5. Swimming Human body displaces water; buoyancy reduces effective weight
6. Life jackets Low-density foam displaces water, adding upward force
7. Helium balloons Helium displaces air; buoyancy exceeds balloon weight
8. Dead Sea floating High salinity → high ( \rho_f ) → greater buoyancy
9. Fish swim bladders Gas-filled bladders adjust buoyancy at different depths
10. Hydrometers Float at depth calibrated to liquid density

Summary

Question Answer
What is buoyant force? Upward linear force from fluid pressure difference on immersed body
What law describes it? Archimedes’ Principle: ( F_b = \rho_f g V_d )
What type of force? Mid Displacement (linear, Rule 1 + 3)
What drives it? Pressure gradient (deeper = higher pressure)
Real examples? Ships, submarines, balloons, icebergs, swimming
What’s its rotational counterpart? Cohesive Adhesive (Mid Cohesion)

Bottom line: Buoyant force is the linear, upward push of a fluid displacing itself around an immersed body — the Mid Displacement force that pairs with cohesive adhesive’s rotational binding in Superphysics’ Liquid Relationalities.

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