Metacentric Height given Moment of Inertia Calculator

✖Moment of Inertia of Waterline Area at a free surface of floating-level about an axis passing through the center of area.ⓘ Moment of Inertia of Waterline Area [I_w]			+10% -10%
✖Volume of Liquid Displaced By Body is the total volume of the liquid which is displaced the immersed/floating body.ⓘ Volume of Liquid Displaced By Body [V_d]			+10% -10%
✖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.ⓘ Distance Between Point B And G [B_g]			+10% -10%

✖Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.ⓘ Metacentric Height given Moment of Inertia [G_m]

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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
G_m = I_w/V_d-B_g
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: 1455 Millimeter --> 1.455 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G_m = I_w/V_d-B_g --> 100/56-1.455

Evaluating ... ...

G_m = 0.330714285714286

STEP 3: Convert Result to Output's Unit

0.330714285714286 Meter -->330.714285714286 Millimeter (Check conversion here)

FINAL ANSWER

330.714285714286 ≈ 330.7143 Millimeter <-- Metacentric Height

(Calculation completed in 00.004 seconds)

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< Hydrostatic Fluid Calculators

Force Acting in x Direction in Momentum Equation

LaTeX 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

LaTeX 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))

Fluid Dynamic or Shear Viscosity Formula

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

Center of Gravity

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

Metacentric Height given Moment of Inertia Formula

LaTeX Go

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

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 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 G_m 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 (I_w), Volume of Liquid Displaced By Body (V_d) & Distance Between Point B And G (B_g) and hit the calculate button. Here is how the Metacentric Height given Moment of Inertia calculation can be explained with given input values -> 330714.3 = 100/56-1.455.

FAQ

What is Metacentric Height given Moment of Inertia?

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 and is represented as G_m = I_w/V_d-B_g 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 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 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 (I_w), Volume of Liquid Displaced By Body (V_d) & Distance Between Point B And G (B_g). 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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