Metacenter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy
M = I/(VO*G)-B
This formula uses 5 Variables
Variables Used
Metacenter - Metacenter is denoted by Mcenter symbol.
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: 1.13 --> No Conversion Required
Centre of Buoyancy: 11 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
M = I/(VO*G)-B --> 1.125/(54*1.13)-11
Evaluating ... ...
M = -10.9815634218289
STEP 3: Convert Result to Output's Unit
-10.9815634218289 --> No Conversion Required
FINAL ANSWER
-10.9815634218289 -10.981563 <-- Metacenter
(Calculation completed in 00.004 seconds)

Credits

Created by Anirudh Singh
National Institute of Technology (NIT), Jamshedpur
Anirudh Singh has created this Calculator and 300+ more calculators!
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19 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(Acceleration Due to Gravity*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))
Center of Buoyancy
Go Centre of Buoyancy = Moment of Inertia/(Volume of Object*Centre of Gravity)-Metacenter
Metacenter
Go Metacenter = Moment of Inertia/(Volume of Object*Centre of Gravity)-Centre of Buoyancy
Theoretical Velocity for Pitot Tube
Go Theoretical Velocity = sqrt(2*Acceleration Due to Gravity*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)
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/(VO*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 (VO), 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 -> -0.081563 = 1.125/(54*1.13)-11.

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/(VO*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 (VO), 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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