Buoyancy and Displaced Fluid

What you’ll learn

Calculate upthrust using displaced volume.

គណនាកម្លាំងអណ្ដែតដោយមាឌអង្គធាតុរាវដែលជំនួស។

Meaning and use

The buoyant force equals the weight of displaced fluid. Use fluid density and submerged volume, not automatically the full object volume. A floating object at rest has upthrust balancing its weight. A fully submerged object need not float or be in equilibrium.

កម្លាំងអណ្ដែតស្មើទម្ងន់អង្គធាតុរាវដែលវត្ថុជំនួស។ ប្រើម៉ាសមាឌអង្គធាតុរាវ និងមាឌលិច។ វត្ថុអណ្ដែតស្ងៀមមានកម្លាំងអណ្ដែតស្មើទម្ងន់។

Formulas

Archimedes’ principle

\[F_b=\rho_{\mathrm{fluid}}gV_{\mathrm{displaced}}\]

Floating equilibrium

\[F_b=mg\]

Symbols and units

Symbol	Meaning	Unit or restriction
Fb	Buoyant force magnitude	N
ρfluid	Density of surrounding fluid	kg/m³
Vdisplaced	Submerged displaced-fluid volume	m³
g	Gravitational field strength	N/kg

Conditions and limits

• The hydrostatic model assumes an approximately uniform fluid density.
• Use submerged volume; for a fully immersed object it equals the external immersed volume.
• ឧទាហរណ៍ប្រើ g=10 N/kg និងម៉ាសមាឌទឹក 1000 kg/m³។

Worked examples

A fully immersed volume

Displaced water volume is 0.002 m³.

1. Calculate \(F_b=1000\times10\times0.002=20\) N.

20 N

កម្លាំងអណ្ដែតអាស្រ័យលើទឹកដែលត្រូវបានជំនួស។

A floating object

A 3 kg object floats at rest in water.

1. Weight \(mg=3\times10=30\) N.
2. Upthrust equals 30 N.
3. Displaced volume \(V=30/(1000\times10)=0.003\) m³.

30 N upthrust; 0.003 m³ displaced

លំនឹងអណ្ដែតឱ្យរកមាឌលិចតាមទម្ងន់។

Common mistakes

Instead of	Use	Why
Use the object’s density in Fb = ρgV.	Use the fluid’s density.	The principle concerns displaced fluid weight.
A partly floating object displaces its full volume.	It displaces only its submerged volume.	The above-water portion does not displace water.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Find buoyancy for 0.001 m³ displaced water, ρ = 1000 kg/m³, g = 10 N/kg.
2. A 2 kg object floats at rest with g = 10 N/kg. Find upthrust.
3. Which volume is used for a partly immersed object?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 10 N

   1000 × 10 × 0.001 = 10.

2. 20 N

   It balances the weight.

3. The submerged displaced-fluid volume.

   Do not substitute the full volume unless fully immersed.

Quick recap

• Use fluid density.
• Use displaced volume.
• Apply force balance only when equilibrium is stated.