Volume of body in fluid for metacentric height and BG Calculator

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Buoyancy

Forces on Submerged Bodies

✖Moment of inertia of plain floating body is a measure of the 'efficiency' of a shape to resist bending caused by loading. The second moment of area is a measure of a shape's resistance to change.ⓘ Moment of Inertia of Plain Floating Body [I]			+10% -10%
✖The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body.ⓘ Metacentric Height of Floating Body [GM]			+10% -10%
✖The Distance of CG from Center of Buoyancy is the distance between the center of gravity and center of buoyancy of a floating body.ⓘ Distance of CG from Center of Buoyancy [BG]			+10% -10%

✖Volume of body submerged in water is the volume of the object that is immersed in the water.ⓘ Volume of body in fluid for metacentric height and BG [V_T]

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Volume of body in fluid for metacentric height and BG

Formula

`"V"_{"T"} = "I"/("GM"+"BG")`

Example

`"12.5m³"="11.25m⁴"/("0.7m"+"0.2m")`

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Volume of body in fluid for metacentric height and BG Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy)
V_T = I/(GM+BG)
This formula uses 4 Variables

Variables Used

Volume of Body Submerged in Water - (Measured in Cubic Meter) - Volume of body submerged in water is the volume of the object that is immersed in the water.
Moment of Inertia of Plain Floating Body - (Measured in Meter⁴) - Moment of inertia of plain floating body is a measure of the 'efficiency' of a shape to resist bending caused by loading. The second moment of area is a measure of a shape's resistance to change.
Metacentric Height of Floating Body - (Measured in Meter) - The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body.
Distance of CG from Center of Buoyancy - (Measured in Meter) - The Distance of CG from Center of Buoyancy is the distance between the center of gravity and center of buoyancy of a floating body.

STEP 1: Convert Input(s) to Base Unit

Moment of Inertia of Plain Floating Body: 11.25 Meter⁴ --> 11.25 Meter⁴ No Conversion Required
Metacentric Height of Floating Body: 0.7 Meter --> 0.7 Meter No Conversion Required
Distance of CG from Center of Buoyancy: 0.2 Meter --> 0.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_T = I/(GM+BG) --> 11.25/(0.7+0.2)

Evaluating ... ...

V_T = 12.5

STEP 3: Convert Result to Output's Unit

12.5 Cubic Meter --> No Conversion Required

FINAL ANSWER

12.5 Cubic Meter <-- Volume of Body Submerged in Water

(Calculation completed in 00.004 seconds)

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< 11 Buoyancy Calculators

Meta-centric height in experimental method

Go Metacentric Height of Floating Body = ((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*tan(Angle of Heel)))

Angle of heel for metacentric height in experimental method

Go Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body))

Movable weight for metacentric height in experimental method

Go Movable Weight on Floating Vessel = (Metacentric Height of Floating Body*Weight of Floating Vessel*tan(Angle of Heel))/(Distance Travelled by Weight on Vessel)

Time Period of Oscillation of Ship

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

Radius of gyration for metacentric height and time period of oscillation

Go Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi)

Volume of body in fluid for metacentric height and BG

Go Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy)

Meta-centric height for time period of oscillation and radius of gyration

Go Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g])

Archimedes Principle

Go Archimedes Principle = Density*Acceleration Due to Gravity*Velocity

Volume of fluid displaced

Go Volume of Fluid Displaced by Body = (Weight of Displaced Fluid)/(Density of Displaced Fluid)

Centre of Buoyancy

Go Centre of Buoyancy for Floating Body = (Depth of Immersed Object in Water)/2

Buoyant Force

Go Buoyant Force = Pressure*Area

Volume of body in fluid for metacentric height and BG Formula

Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy)
V_T = I/(GM+BG)

What is meta-centre and BG?

It is defined as the point about which a body starts oscillating when the body is tilted by a small angle. The location of centre of gravity and centre of buoyancy is the positions G and B.

What is meta-centric height?

The distance between the meta-centre of a floating body and the center of gravity of the body is called meta-centric height. It is calculated using analytical and theoretical methods.

How to Calculate Volume of body in fluid for metacentric height and BG?

Volume of body in fluid for metacentric height and BG calculator uses Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy) to calculate the Volume of Body Submerged in Water, The Volume of body in fluid for metacentric height and BG is defined as the moment of inertia of the plan of the body to the metacentric height and distance between the positions (BG). Volume of Body Submerged in Water is denoted by V_T symbol.

How to calculate Volume of body in fluid for metacentric height and BG using this online calculator? To use this online calculator for Volume of body in fluid for metacentric height and BG, enter Moment of Inertia of Plain Floating Body (I), Metacentric Height of Floating Body (GM) & Distance of CG from Center of Buoyancy (BG) and hit the calculate button. Here is how the Volume of body in fluid for metacentric height and BG calculation can be explained with given input values -> 12.5 = 11.25/(0.7+0.2).

FAQ

What is Volume of body in fluid for metacentric height and BG?

The Volume of body in fluid for metacentric height and BG is defined as the moment of inertia of the plan of the body to the metacentric height and distance between the positions (BG) and is represented as V_T = I/(GM+BG) or Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy). Moment of inertia of plain floating body is a measure of the 'efficiency' of a shape to resist bending caused by loading. The second moment of area is a measure of a shape's resistance to change, The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body & The Distance of CG from Center of Buoyancy is the distance between the center of gravity and center of buoyancy of a floating body.

How to calculate Volume of body in fluid for metacentric height and BG?

The Volume of body in fluid for metacentric height and BG is defined as the moment of inertia of the plan of the body to the metacentric height and distance between the positions (BG) is calculated using Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy). To calculate Volume of body in fluid for metacentric height and BG, you need Moment of Inertia of Plain Floating Body (I), Metacentric Height of Floating Body (GM) & Distance of CG from Center of Buoyancy (BG). With our tool, you need to enter the respective value for Moment of Inertia of Plain Floating Body, Metacentric Height of Floating Body & Distance of CG from Center 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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