Buoyant Force

Unit 2 Displacement

Buoyant Force

Juan Juan
12 min read
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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:

SymbolMeaningUnit
Fb F_b Buoyant force (upward)N \text{N}
ρf \rho_f Fluid densitykg/m3 \text{kg}/\text{m}^3
gGravitational accelerationm/s2 \text{m}/\text{s}^2
Vd V_d Displaced fluid volumem3 \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:

SymbolMeaningUnit
∮S \oint_{\mathcal{S}} Surface integral over the body—
PHydrostatic pressure at depthPa \text{Pa}
dA d\mathbf{A} Outward area elementm2 \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

PropertyExplanation
DirectionalAlways acts vertically upward
LinearPushes along a straight line opposing gravity
Volume-dependentDepends on displaced fluid volume, not body mass
Density-dependentHeavier fluids produce greater buoyancy
Depth-independentNet buoyancy same at any depth (for incompressible fluid)
Pressure-drivenArises from pressure gradient across body height
RestoringReturns 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

ExampleHow Buoyant Force Works
1. Ships floatingHull displaces water; buoyancy balances ship’s weight
2. Submarines divingBallast tanks fill with water, reducing buoyancy
3. Hot air balloonsHeated air is less dense; displaced cool air pushes balloon up
4. Icebergs~90% submerged because ice density is ~90% of water
5. SwimmingHuman body displaces water; buoyancy reduces effective weight
6. Life jacketsLow-density foam displaces water, adding upward force
7. Helium balloonsHelium displaces air; buoyancy exceeds balloon weight
8. Dead Sea floatingHigh salinity → high ( \rho_f ) → greater buoyancy
9. Fish swim bladdersGas-filled bladders adjust buoyancy at different depths
10. HydrometersFloat at depth calibrated to liquid density

Summary

QuestionAnswer
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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