Experimental Determination of Metacentric height Calculator

✖Movable weight on ship is the weight that can be moved from one place to another place on a ship.ⓘ Movable Weight on Ship [W']			+10% -10%
✖Transverse Displacement of the weight "W" can be calculated by multiplying shear strain with height.ⓘ Transverse Displacement [x]			+10% -10%
✖Ship weight is the weight of the ship alone without any load on the ship.ⓘ Ship Weight [W]			+10% -10%
✖Angle of tilt is the angle tilted by the ship during sailing.ⓘ Angle of Tilt [Θ]			+10% -10%

✖Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.ⓘ Experimental Determination of Metacentric height [GM]

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Formula

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Experimental Determination of Metacentric height

Formula

`"GM" = ("W'"*"x")/(("W'"+"W")*tan("Θ"))`

Example

`"330.2655mm"=("43.5kg"*"38400mm")/(("43.5kg"+"25500kg")*tan("11.2°"))`

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Experimental Determination of Metacentric height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))
GM = (W'*x)/((W'+W)*tan(Θ))
This formula uses 1 Functions, 5 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

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.
Movable Weight on Ship - (Measured in Kilogram) - Movable weight on ship is the weight that can be moved from one place to another place on a ship.
Transverse Displacement - (Measured in Meter) - Transverse Displacement of the weight "W" can be calculated by multiplying shear strain with height.
Ship Weight - (Measured in Kilogram) - Ship weight is the weight of the ship alone without any load on the ship.
Angle of Tilt - (Measured in Radian) - Angle of tilt is the angle tilted by the ship during sailing.

STEP 1: Convert Input(s) to Base Unit

Movable Weight on Ship: 43.5 Kilogram --> 43.5 Kilogram No Conversion Required
Transverse Displacement: 38400 Millimeter --> 38.4 Meter (Check conversion here)
Ship Weight: 25500 Kilogram --> 25500 Kilogram No Conversion Required
Angle of Tilt: 11.2 Degree --> 0.195476876223328 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

GM = (W'*x)/((W'+W)*tan(Θ)) --> (43.5*38.4)/((43.5+25500)*tan(0.195476876223328))

Evaluating ... ...

GM = 0.330265486594649

STEP 3: Convert Result to Output's Unit

0.330265486594649 Meter -->330.265486594649 Millimeter (Check conversion here)

FINAL ANSWER

330.265486594649 ≈ 330.2655 Millimeter <-- Metacentric Height

(Calculation completed in 00.004 seconds)

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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(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)

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

Experimental Determination of Metacentric height Formula

Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))
GM = (W'*x)/((W'+W)*tan(Θ))

what is a metacenter?

Metacentre is the theoretical point at which an imaginary vertical line passing through the centre of buoyancy and centre of gravity intersects the imaginary vertical line through a new centre of buoyancy created when the body is displaced, or tipped, in the water.

How to Calculate Experimental Determination of Metacentric height?

Experimental Determination of Metacentric height calculator uses Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)) to calculate the Metacentric Height, Experimental determination of Metacentric height is determining the metacentric height by experimental procedure. Metacentric Height is denoted by GM symbol.

How to calculate Experimental Determination of Metacentric height using this online calculator? To use this online calculator for Experimental Determination of Metacentric height, enter Movable Weight on Ship (W'), Transverse Displacement (x), Ship Weight (W) & Angle of Tilt (Θ) and hit the calculate button. Here is how the Experimental Determination of Metacentric height calculation can be explained with given input values -> 772646.1 = (43.5*38.4)/((43.5+25500)*tan(0.195476876223328)).

FAQ

What is Experimental Determination of Metacentric height?

Experimental determination of Metacentric height is determining the metacentric height by experimental procedure and is represented as GM = (W'*x)/((W'+W)*tan(Θ)) or Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)). Movable weight on ship is the weight that can be moved from one place to another place on a ship, Transverse Displacement of the weight "W" can be calculated by multiplying shear strain with height, Ship weight is the weight of the ship alone without any load on the ship & Angle of tilt is the angle tilted by the ship during sailing.

How to calculate Experimental Determination of Metacentric height?

Experimental determination of Metacentric height is determining the metacentric height by experimental procedure is calculated using Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)). To calculate Experimental Determination of Metacentric height, you need Movable Weight on Ship (W'), Transverse Displacement (x), Ship Weight (W) & Angle of Tilt (Θ). With our tool, you need to enter the respective value for Movable Weight on Ship, Transverse Displacement, Ship Weight & Angle of Tilt 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 Movable Weight on Ship, Transverse Displacement, Ship Weight & Angle of Tilt. We can use 2 other way(s) to calculate the same, which is/are as follows -

Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G
Metacentric Height = Distance between Point B and M-Distance Between Point B and G

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