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Metacenter Formula

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Metacenter is the theoretical point where a vertical line through the center of buoyancy and center of gravity intersects the new center of buoyancy when a body is tilted in water. Check FAQs

M = \frac{I}{V o \cdot G} - B

M - Metacenter?I - Moment of Inertia?V_o - Volume of Object?G - Centre of Gravity?B - Centre of Buoyancy?

Metacenter Example

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Here is how the Metacenter equation looks like with Values.

Here is how the Metacenter equation looks like with Units.

Here is how the Metacenter equation looks like.

16.9921 = \frac{1.125}{54 \cdot 0.021} - -16

16.9921 = \frac{1.125kg·m²}{54m³ \cdot 0.021} - -16

16.9921 = \frac{1.125}{54 \cdot 0.021} - -16

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Metacenter Solution

Follow our step by step solution on how to calculate Metacenter?

FIRST Step Consider the formula

M = \frac{I}{V o \cdot G} - B

Next Step Substitute values of Variables

∴

M = \frac{1.125kg·m²}{54m³ \cdot 0.021} - -16

Next Step Prepare to Evaluate

∴

M = \frac{1.125}{54 \cdot 0.021} - -16

Next Step Evaluate

∴

M = 16.9920634920635

LAST Step Rounding Answer

∴

M = 16.9921

Metacenter Formula Elements

Variables

Metacenter

Metacenter is the theoretical point where a vertical line through the center of buoyancy and center of gravity intersects the new center of buoyancy when a body is tilted in water.

Symbol: M

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Metacenter

Moment of Inertia

Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.

Symbol: I

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of Inertia

Volume of Object

Volume of Object is the volume occupied by a submerged or floating object in a fluid.

Symbol: V_o

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Object

Centre of Gravity

Centre of gravity of the object is the point through which gravitational force is acting.

Symbol: G

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Centre of Gravity

Centre of Buoyancy

Centre of Buoyancy is the center of the gravity of the volume of water which a body displaces.

Symbol: B

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Centre of Buoyancy

Other formulas in Hydrostatic Fluid category

Go Force Acting in y-Direction in Momentum Equation

F y = ρ l \cdot Q \cdot (- V 2 \cdot \sin (θ) - P 2 \cdot A 2 \cdot \sin (θ))

Go Force Acting in x Direction in Momentum Equation

F x = ρ l \cdot Q \cdot (V 1 - V 2 \cdot \cos (θ)) + P 1 \cdot A 1 - (P 2 \cdot A 2 \cdot \cos (θ))

Go Fluid Dynamic or Shear Viscosity Formula

μ = \frac{F a \cdot r}{A \cdot P s}

Go Center of Gravity

G = \frac{I}{V o \cdot (B + M)}

How to Evaluate Metacenter?

Metacenter evaluator uses Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy to evaluate the Metacenter, Metacenter, also spelled metacenter, in fluid mechanics, the theoretical point at which an imaginary vertical line passing through the center of buoyancy and center of gravity intersects the imaginary vertical line through a new center of buoyancy created when the body is displaced, or tipped, in the water. Metacenter is denoted by M symbol.

How to evaluate Metacenter using this online evaluator? To use this online evaluator for Metacenter, enter Moment of Inertia (I), Volume of Object (V_o), Centre of Gravity (G) & Centre of Buoyancy (B) and hit the calculate button.

FAQs on Metacenter

What is the formula to find Metacenter?

The formula of Metacenter is expressed as Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy. Here is an example- 16.99206 = 1.125/(54*0.021)-(-16).

How to calculate Metacenter?

With Moment of Inertia (I), Volume of Object (V_o), Centre of Gravity (G) & Centre of Buoyancy (B) we can find Metacenter using the formula - Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy.

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Metacenter Formula

Metacenter Example

Metacenter Solution

Metacenter Formula Elements

Other formulas in Hydrostatic Fluid category

How to Evaluate Metacenter?

FAQs on Metacenter

Variable Name