Metacentric Height given Moment of Inertia Solution

STEP 0: Pre-Calculation Summary
Formula Used
Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G
GM = Iwl/VD-BG
This formula uses 4 Variables
Variables Used
Metacentric Height - (Measured in Meter) - Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.
Moment of Inertia of Waterline Area - (Measured in Kilogram Square Meter) - Moment of inertia of waterline area at a free surface of floating-level about an axis passing through the center of area.
Volume of Liquid Displaced by Body - (Measured in Cubic Meter) - Volume of Liquid displaced by Body is the total volume of the liquid which is displaced the immersed/floating body.
Distance Between Point B and G - (Measured in Meter) - 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.
STEP 1: Convert Input(s) to Base Unit
Moment of Inertia of Waterline Area: 100 Kilogram Square Meter --> 100 Kilogram Square Meter No Conversion Required
Volume of Liquid Displaced by Body: 56 Cubic Meter --> 56 Cubic Meter No Conversion Required
Distance Between Point B and G: 1500 Millimeter --> 1.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
GM = Iwl/VD-BG --> 100/56-1.5
Evaluating ... ...
GM = 0.285714285714286
STEP 3: Convert Result to Output's Unit
0.285714285714286 Meter -->285.714285714286 Millimeter (Check conversion here)
FINAL ANSWER
285.714285714286 285.7143 Millimeter <-- Metacentric Height
(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath
Osmania University (OU), Hyderabad
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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

Metacentric Height given Moment of Inertia Formula

Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G
GM = Iwl/VD-BG

What is metacentric height?

The vertical distance between G and M is referred to as the metacentric height. The relative positions of vertical centre of gravity G and the initial metacentre M are extremely important with regard to their effect on the ship's stability.

How to Calculate Metacentric Height given Moment of Inertia?

Metacentric Height given Moment of Inertia calculator uses Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G to calculate the Metacentric Height, Metacentric Height given Moment of Inertia is the vertical distance between the center of gravity of the body and the metacenter of that body. Where B stands for center of buoyancy and G stands for center of gravity. Metacentric Height is denoted by GM symbol.

How to calculate Metacentric Height given Moment of Inertia using this online calculator? To use this online calculator for Metacentric Height given Moment of Inertia, enter Moment of Inertia of Waterline Area (Iwl), Volume of Liquid Displaced by Body (VD) & Distance Between Point B and G (BG) and hit the calculate button. Here is how the Metacentric Height given Moment of Inertia calculation can be explained with given input values -> 285714.3 = 100/56-1.5.

FAQ

What is Metacentric Height given Moment of Inertia?
Metacentric Height given Moment of Inertia is the vertical distance between the center of gravity of the body and the metacenter of that body. Where B stands for center of buoyancy and G stands for center of gravity and is represented as GM = Iwl/VD-BG or Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G. Moment of inertia of waterline area at a free surface of floating-level about an axis passing through the center of area, Volume of Liquid displaced by Body is the total volume of the liquid which is displaced the immersed/floating body & 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.
How to calculate Metacentric Height given Moment of Inertia?
Metacentric Height given Moment of Inertia is the vertical distance between the center of gravity of the body and the metacenter of that body. Where B stands for center of buoyancy and G stands for center of gravity is calculated using Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G. To calculate Metacentric Height given Moment of Inertia, you need Moment of Inertia of Waterline Area (Iwl), Volume of Liquid Displaced by Body (VD) & Distance Between Point B and G (BG). With our tool, you need to enter the respective value for Moment of Inertia of Waterline Area, Volume of Liquid Displaced by Body & Distance Between Point B and G and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Metacentric Height?
In this formula, Metacentric Height uses Moment of Inertia of Waterline Area, Volume of Liquid Displaced by Body & Distance Between Point B and G. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))
  • Metacentric Height = Distance between Point B and M-Distance Between Point B and G
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