Set object shape, density, fluid type and submersion ratio to compute buoyant force, weight and apparent weight in real time. Visualize Archimedes' principle with interactive force arrows.
Parameters
Object Shape
Side length a
m
Height h
m
Object density ρobj
kg/m³
Wood:500 / Aluminum:2700 / Steel:7800
Fluid type
Fluid density ρf
kg/m³
Submersion ratio
%
Results
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Buoyancy F_b [N]
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Weight W [N]
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Net force [N]
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Apparent weight [N]
Status—
Visualization
Theory & Key Formulas
Archimedes' principle:
$$F_b = \rho_f \cdot g \cdot V_{sub}$$
Weight: $W = \rho_{obj}\cdot g \cdot V$
Apparent weight: $W_{app}= W - F_b = (\rho_{obj}- \rho_f) \cdot g \cdot V_{sub}$
What exactly is buoyant force? I know things float, but what's the physics behind it?
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Basically, it's an upward force a fluid exerts on any object placed in it. It happens because pressure increases with depth—the pressure on the bottom of the object is greater than on the top, creating a net upward push. In this simulator, that's the $F_b$ value you see update when you change the Fluid type or the Submersion ratio slider.
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Wait, really? So if I make the object denser, it just sinks and the buoyant force disappears?
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Not quite! The buoyant force only depends on the fluid and how much object volume is submerged ($V_{sub}$). Try it: increase the Object density ρ slider. The weight ($W$) goes up, but $F_b$ stays the same if the object is fully submerged. The object sinks because $W$ becomes greater than $F_b$.
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So what's "apparent weight"? Is that just the weight minus the buoyant force?
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Exactly! $W_{app}= W - F_b$. It's what a scale would read if the object was submerged. For instance, lifting a rock underwater feels easier. In the simulator, watch the $W_{app}$ value become zero when the object is neutrally buoyant—that's the key principle for designing submarines! Play with the Object Shape and Side length a to see how volume changes everything.
Physical Model & Key Equations
The fundamental principle is Archimedes' principle. The magnitude of the buoyant force is equal to the weight of the fluid displaced by the object.
$$F_b = \rho_f \cdot g \cdot V_{sub}$$
Where:
$F_b$ = Buoyant force (N)
$\rho_f$ = Density of the fluid (kg/m³)
$g$ = Acceleration due to gravity (9.81 m/s²)
$V_{sub}$ = Volume of the object submerged in the fluid (m³)
To determine if an object floats, sinks, or is neutrally buoyant, we compare $F_b$ to the object's actual weight. The apparent weight is the net force.
$$W = \rho_{obj}\cdot g \cdot V_{total}$$
$$W_{app}= W - F_b$$
Where:
$W$ = True weight of object (N)
$\rho_{obj}$ = Density of the object (kg/m³)
$V_{total}$ = Total volume of the object (m³)
$W_{app}$ = Apparent weight in the fluid (N). If $W_{app}< 0$, the object rises; if $W_{app}> 0$, it sinks.
Frequently Asked Questions
Yes, a submersion rate of 100% means the entire object is within the fluid. In this case, the volume of fluid displaced equals the total volume of the object, generating the maximum buoyant force. If the buoyant force exceeds gravity, the object will float upward; if it is less, the object will sink.
No, an object with a density lower than that of the fluid will still float upward even when fully submerged, because the buoyant force exceeds gravity. In this simulator, changing the submersion rate does not alter the object's density, so the determination of floating or sinking is based on the density difference.
A negative apparent weight indicates that the buoyant force exceeds gravity. Underwater, the object experiences an upward force and tends to float, so when measured with a spring scale, it would be observed as a negative weight (an upward pushing force).
Seawater has a density about 3% higher than water (approximately 1025 kg/m³), so even with the same submerged volume, the mass of fluid displaced increases. According to Archimedes' principle, buoyant force is proportional to fluid density, so seawater generates a greater buoyant force.
Real-World Applications
Ship & Offshore Platform Design: Naval architects must precisely balance weight and buoyancy to ensure ships float at the correct waterline (draft). For offshore oil platforms, massive buoyant hulls support decks weighing thousands of tons. Engineers use these exact calculations to determine stability.
Submarine & ROV Control: Submersibles use ballast tanks to change their overall density. To dive, they take in water (increasing $W$); to surface, they pump it out and replace it with air (decreasing $W$). Achieving neutral buoyancy ($W_{app}=0$) allows them to hover at depth.
Hot Air & Helium Balloons: The "fluid" here is air. Heating the air inside the balloon decreases its density ($\rho_{obj}$). When the balloon's overall density becomes less than the surrounding air ($\rho_f$), the buoyant force exceeds its weight, and it rises.
CAE & CFD Preprocessing: Before running complex fluid simulations in ANSYS Fluent or OpenFOAM, engineers perform buoyancy checks. Setting the correct buoyancy term $\rho_f g$ is crucial for accurately modeling natural convection, underwater vehicle dynamics, or the settling of particles in a tank.
Common Misconceptions and Points to Note
Let's go over some points where beginners often get tripped up when mastering this tool. First, "Density and Weight Units". The tool defaults to kg/m³ and N (Newtons), but in practice, you'll often use g/cm³ or kgf (kilogram-force). For example, if you input the density of iron as 7.8 g/cm³, the tool correctly interprets it as 7800 kg/m³. However, when you want to get a tangible sense of the "apparent weight", converting the result from N to kgf by multiplying by approximately 0.102 makes it easier to visualize as "weight".
Next, the concept of "Complete Submersion vs. Partial Floating". If the object density is greater than the fluid density, the object sinks completely. In this case, the submersion rate is fixed at 100%, and buoyancy is calculated based on the object's *entire volume*. Conversely, if the object density is smaller, the tool automatically calculates the floating height (submersion rate), but this is for a static, settled state. If you actually push an ice cube down into water, the submersion rate temporarily increases and the apparent weight changes. Be careful not to confuse this "dynamic process" with the "static result".
Finally, "Real-World Interpretation of Shape Parameters". For instance, setting a cylinder's "height" to 1m and diameter to 0.1m creates a long, thin rod. Whether you place it vertically or horizontally in water changes its actual floating behavior, but the tool's calculation depends solely on the submerged volume $V_{sub}$. Remember, it calculates an isotropic buoyant force, so it does not account for stability (e.g., metacentric height, etc.).