Metacenter Calculator

✖Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.ⓘ Moment of Inertia [I]			+10% -10%
✖Volume of Object is the volume occupied by a submerged or floating object in a fluid.ⓘ Volume of Object [V_o]			+10% -10%
✖Centre of gravity of the object is the point through which gravitational force is acting.ⓘ Centre of Gravity [G]			+10% -10%
✖Centre of Buoyancy is the center of the gravity of the volume of water which a body displaces.ⓘ Centre of Buoyancy [B]			+10% -10%

✖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.ⓘ Metacenter [M]

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Formula

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Metacenter

Formula

`"M" = "I"/("V"_{"o"}*"G")-"B"`

Example

`"16.99206"="1.125kg·m²"/("54m³"*"0.021")-"-16"`

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Metacenter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy
M = I/(V_o*G)-B
This formula uses 5 Variables

Variables Used

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.
Moment of Inertia - (Measured in Kilogram Square Meter) - Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis.
Volume of Object - (Measured in Cubic Meter) - Volume of Object is the volume occupied by a submerged or floating object in a fluid.
Centre of Gravity - Centre of gravity of the object is the point through which gravitational force is acting.
Centre of Buoyancy - Centre of Buoyancy is the center of the gravity of the volume of water which a body displaces.

STEP 1: Convert Input(s) to Base Unit

Moment of Inertia: 1.125 Kilogram Square Meter --> 1.125 Kilogram Square Meter No Conversion Required
Volume of Object: 54 Cubic Meter --> 54 Cubic Meter No Conversion Required
Centre of Gravity: 0.021 --> No Conversion Required
Centre of Buoyancy: -16 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M = I/(V_o*G)-B --> 1.125/(54*0.021)-(-16)

Evaluating ... ...

M = 16.9920634920635

STEP 3: Convert Result to Output's Unit

16.9920634920635 --> No Conversion Required

FINAL ANSWER

16.9920634920635 ≈ 16.99206 <-- Metacenter

(Calculation completed in 00.004 seconds)

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Created by Anirudh Singh

National Institute of Technology (NIT), Jamshedpur

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< 20 Hydrostatic Fluid Calculators

Force Acting in x Direction in Momentum Equation

Go Force in X Direction = Density of Liquid*Discharge*(Velocity at Section 1-1-Velocity at Section 2-2*cos(Theta))+Pressure at Section 1*Cross Sectional Area at Point 1-(Pressure at Section 2*Cross Sectional Area at Point 2*cos(Theta))

Force Acting in y-Direction in Momentum Equation

Go Force in Y Direction = Density of Liquid*Discharge*(-Velocity at Section 2-2*sin(Theta)-Pressure at Section 2*Cross Sectional Area at Point 2*sin(Theta))

Experimental Determination of Metacentric height

Go Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))

Radius of Gyration given Time Period of Rolling

Go Radius of Gyration = sqrt([g]*Metacentric Height*(Time Period of Rolling/2*pi)^2)

Fluid Dynamic or Shear Viscosity Formula

Go Dynamic Viscosity = (Applied Force*Distance Between Two Masses)/(Area of Solid Plates*Peripheral Speed)

Moment of Inertia of Waterline Area using Metacentric Height

Go Moment of Inertia of Waterline Area = (Metacentric Height+Distance Between Point B And G)*Volume of Liquid Displaced By Body

Volume of Liquid Displaced given Metacentric Height

Go Volume of Liquid Displaced By Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B And G)

Distance between Buoyancy Point and Center of Gravity given Metacenter Height

Go Distance Between Point B And G = Moment of Inertia of Waterline Area/Volume of Liquid Displaced By Body-Metacentric Height

Metacentric Height given Moment of Inertia

Go Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced By Body-Distance Between Point B And G

Center of Gravity

Go Centre of Gravity = Moment of Inertia/(Volume of Object*(Centre of Buoyancy+Metacenter))

Metacenter

Go Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy

Center of Buoyancy

Go Centre of Buoyancy = (Moment of Inertia/Volume of Object)-Metacenter

Theoretical Velocity for Pitot Tube

Go Theoretical Velocity = sqrt(2*[g]*Dynamic Pressure Head)

Metacentric Height

Go Metacentric Height = Distance Between Point B And M-Distance Between Point B And G

Volume of Submerged Object given Buoyancy Force

Go Volume of Object = Buoyancy Force/Specific Weight of Liquid

Buoyancy Force

Go Buoyancy Force = Specific Weight of Liquid*Volume of Object

Surface Tension given Surface Energy and Area

Go Surface Tension = (Surface Energy)/(Surface Area)

Pressure in Bubble

Go Pressure = (8*Surface Tension)/Diameter of Bubble

Surface Energy given Surface Tension

Go Surface Energy = Surface Tension*Surface Area

Surface Area given Surface Tension

Go Surface Area = Surface Energy/Surface Tension

Metacenter Formula

Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy
M = I/(V_o*G)-B

What is Metacentric Height?

The metacentric height (GM) is a measurement of the initial static stability of a floating body. It is calculated as the distance between the center of gravity of a ship and its metacenter . A larger metacentric height implies greater initial stability against overturning.

How to Calculate Metacenter?

Metacenter calculator uses Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy to calculate 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 calculate Metacenter using this online calculator? To use this online calculator 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. Here is how the Metacenter calculation can be explained with given input values -> 16.99206 = 1.125/(54*0.021)-(-16).

FAQ

What is 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 and is represented as M = I/(V_o*G)-B or Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy. Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis, Volume of Object is the volume occupied by a submerged or floating object in a fluid, Centre of gravity of the object is the point through which gravitational force is acting & Centre of Buoyancy is the center of the gravity of the volume of water which a body displaces.

How to calculate 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 is calculated using Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy. To calculate Metacenter, you need Moment of Inertia (I), Volume of Object (V_o), Centre of Gravity (G) & Centre of Buoyancy (B). With our tool, you need to enter the respective value for Moment of Inertia, Volume of Object, Centre of Gravity & Centre of Buoyancy and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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