Ship Displacement
A floating ship displaces its own weight in water.
Formula
Variables
Example
V=1000 m³ seawater: Δ = 1,025,000 kg
How it works
A floating ship is supported by the buoyant force from the water it pushes aside. At equilibrium, that buoyant force equals the ship's weight, so the mass of displaced water equals the ship's mass. Since mass equals density times volume, the displaced mass is found with Δ = ρV.
When to use it
Use this formula when you need the mass of water displaced by a floating vessel, or when estimating a ship’s draft from its submerged volume and the density of the water. It is also useful for checking whether a loading condition is physically plausible in seawater, freshwater, or mixed water.
Worked example, step by step
A barge has a submerged volume of 620 m³ in freshwater. Take freshwater density as 1,000 kg/m³. Use Δ = ρV. Δ = 1,000 × 620 Δ = 620,000 kg So the barge displaces 620,000 kg of freshwater.
Common mistakes to avoid
- Using the ship’s total volume instead of only the submerged volume
- Mixing up mass and weight, or forgetting that Δ here is in kilograms
- Using the wrong water density, especially confusing freshwater and seawater
Did You Know?
A ship's 'displacement tonnage' is literally the mass of seawater its hull pushes aside.
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