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Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body. Check FAQs
Gm=IwVd-Bg
Gm - Metacentric Height?Iw - Moment of Inertia of Waterline Area?Vd - Volume of Liquid Displaced By Body?Bg - Distance Between Point B And G?

Metacentric Height given Moment of Inertia Example

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Here is how the Metacentric Height given Moment of Inertia equation looks like with Values.

Here is how the Metacentric Height given Moment of Inertia equation looks like with Units.

Here is how the Metacentric Height given Moment of Inertia equation looks like.

330.7143Edit=100Edit56Edit-1455Edit
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HomeIcon Home » Category Engineering » Category Mechanical » Category Fluid Mechanics » fx Metacentric Height given Moment of Inertia

Metacentric Height given Moment of Inertia Solution

Follow our step by step solution on how to calculate Metacentric Height given Moment of Inertia?

FIRST Step Consider the formula
Gm=IwVd-Bg
Next Step Substitute values of Variables
∴ Gm=100kg·m²56m³-1455mm
Next Step Convert Units
∴ Gm=100kg·m²56m³-1.455m
Next Step Prepare to Evaluate
∴ Gm=10056-1.455
Next Step Evaluate
∴Gm=0.330714285714286m
Next Step Convert to Output's Unit
∴Gm=330.714285714286mm
LAST Step Rounding Answer
∴Gm=330.7143mm

Metacentric Height given Moment of Inertia Formula Elements

Variables
Metacentric Height
Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.
Symbol: Gm
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Metacentric HeightOpen Variable
Moment of Inertia of Waterline Area
Moment of Inertia of Waterline Area at a free surface of floating-level about an axis passing through the center of area.
Symbol: Iw
Measurement: Moment of InertiaUnit: kg·m²
Note: Value should be greater than 0.
Formulas to find Moment of Inertia of Waterline AreaOpen Variable
Volume of Liquid Displaced By Body
Volume of Liquid Displaced By Body is the total volume of the liquid which is displaced the immersed/floating body.
Symbol: Vd
Measurement: VolumeUnit: m³
Note: Value can be positive or negative.
Formulas to find Volume of Liquid Displaced By BodyOpen Variable
Distance Between Point B And G
Distance Between Point B And G is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.
Symbol: Bg
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Distance Between Point B And GOpen Variable

Other Formulas to find Metacentric Height

​Go Experimental Determination of Metacentric height
Gm=W'⋅x(W'+W)⋅tan(Θ)
​Go Metacentric Height
Gm=Bm-Bg

Other formulas in Hydrostatic Fluid category

​Go Force Acting in y-Direction in Momentum Equation
Fy=ρl⋅Q⋅(-V2⋅sin(θ)-P2⋅A2⋅sin(θ))
​Go Force Acting in x Direction in Momentum Equation
Fx=ρl⋅Q⋅(V1-V2⋅cos(θ))+P1⋅A1-(P2⋅A2⋅cos(θ))
​Go Fluid Dynamic or Shear Viscosity Formula
μ=Fa⋅rA⋅Ps
​Go Center of Gravity
G=IVo⋅(B+M)

How to Evaluate Metacentric Height given Moment of Inertia?

Metacentric Height given Moment of Inertia evaluator uses Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced By Body-Distance Between Point B And G to evaluate the Metacentric Height, Metacentric Height given Moment of Inertia formula is defined as a measure of the distance between the centre of gravity of a floating or submerged body and the metacentre, which is the point where the buoyancy force acts, providing stability to the body in hydrostatic fluid. Metacentric Height is denoted by Gm symbol.

How to evaluate Metacentric Height given Moment of Inertia using this online evaluator? To use this online evaluator for Metacentric Height given Moment of Inertia, enter Moment of Inertia of Waterline Area (Iw), Volume of Liquid Displaced By Body (Vd) & Distance Between Point B And G (Bg) and hit the calculate button.

FAQs on Metacentric Height given Moment of Inertia

What is the formula to find Metacentric Height given Moment of Inertia?
The formula of Metacentric Height given Moment of Inertia is expressed as Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced By Body-Distance Between Point B And G. Here is an example- 330714.3 = 100/56-1.455.
How to calculate Metacentric Height given Moment of Inertia?
With Moment of Inertia of Waterline Area (Iw), Volume of Liquid Displaced By Body (Vd) & Distance Between Point B And G (Bg) we can find Metacentric Height given Moment of Inertia using the formula - Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced By Body-Distance Between Point B And G.
What are the other ways to Calculate Metacentric Height?
Here are the different ways to Calculate Metacentric Height-
  • Metacentric Height=(Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))OpenImg
  • Metacentric Height=Distance Between Point B And M-Distance Between Point B And GOpenImg
Can the Metacentric Height given Moment of Inertia be negative?
No, the Metacentric Height given Moment of Inertia, measured in Length cannot be negative.
Which unit is used to measure Metacentric Height given Moment of Inertia?
Metacentric Height given Moment of Inertia is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Metacentric Height given Moment of Inertia can be measured.
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