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Experimental Determination of Metacentric height Formula

GoMetacentric Height given Moment of Inertia Formula

GoMetacentric Height Formula

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Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body. Check FAQs

G m = \frac{W' \cdot x}{(W' + W) \cdot \tan (Θ)}

G_m - Metacentric Height?W' - Movable Weight on Ship?x - Transverse Displacement?W - Ship Weight?Θ - Angle of Tilt?

Experimental Determination of Metacentric height Example

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Here is how the Experimental Determination of Metacentric height equation looks like with Values.

Here is how the Experimental Determination of Metacentric height equation looks like with Units.

Here is how the Experimental Determination of Metacentric height equation looks like.

330.2655 = \frac{43.5 \cdot 38400}{(43.5 + 25500) \cdot \tan (11.2)}

330.2655mm = \frac{43.5kg \cdot 38400mm}{(43.5kg + 25500kg) \cdot \tan (11.2°)}

330.2655 = \frac{43.5 \cdot 38400}{(43.5 + 25500) \cdot \tan (11.2)}

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Experimental Determination of Metacentric height Solution

Follow our step by step solution on how to calculate Experimental Determination of Metacentric height?

FIRST Step Consider the formula

G m = \frac{W' \cdot x}{(W' + W) \cdot \tan (Θ)}

Next Step Substitute values of Variables

∴

G m = \frac{43.5kg \cdot 38400mm}{(43.5kg + 25500kg) \cdot \tan (11.2°)}

Next Step Convert Units

∴

G m = \frac{43.5kg \cdot 38.4m}{(43.5kg + 25500kg) \cdot \tan (0.1955rad)}

Next Step Prepare to Evaluate

∴

G m = \frac{43.5 \cdot 38.4}{(43.5 + 25500) \cdot \tan (0.1955)}

Next Step Evaluate

∴

G m = 0.330265486594649m

Next Step Convert to Output's Unit

∴

G m = 330.265486594649mm

LAST Step Rounding Answer

∴

G m = 330.2655mm

Experimental Determination of Metacentric height Formula Elements

Variables

Functions

Metacentric Height

Metacentric Height is defined as the vertical distance between the center of gravity of a body and metacenter of that body.

Symbol: G_m

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Metacentric Height

Movable Weight on Ship

Movable Weight on Ship is the weight that can be moved from one place to another place on a ship.

Symbol: W'

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Movable Weight on Ship

Transverse Displacement

Transverse displacement refers to the movement or deviation of a point or object in a direction perpendicular to its primary motion or the longitudinal axis.

Symbol: x

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Transverse Displacement

Ship Weight

Ship weight is the weight of the ship alone without any load on the ship.

Symbol: W

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Ship Weight

Angle of Tilt

Angle of Tilt refers to the inclination of the free surface of the fluid when the domain is subjected to external forces or gradients.

Symbol: Θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Tilt

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.

Syntax: tan(Angle)

Other Formulas to find Metacentric Height

Go Metacentric Height given Moment of Inertia

G m = \frac{I w}{V d} - B g

Go Metacentric Height

G m = B m - B g

Other formulas in Hydrostatic Fluid category

Go Force Acting in y-Direction in Momentum Equation

F y = ρ l \cdot Q \cdot (- V 2 \cdot \sin (θ) - P 2 \cdot A 2 \cdot \sin (θ))

Go Force Acting in x Direction in Momentum Equation

F x = ρ l \cdot Q \cdot (V 1 - V 2 \cdot \cos (θ)) + P 1 \cdot A 1 - (P 2 \cdot A 2 \cdot \cos (θ))

Go Fluid Dynamic or Shear Viscosity Formula

μ = \frac{F a \cdot r}{A \cdot P s}

Go Center of Gravity

G = \frac{I}{V o \cdot (B + M)}

How to Evaluate Experimental Determination of Metacentric height?

Experimental Determination of Metacentric height evaluator uses Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)) to evaluate the Metacentric Height, Experimental Determination of Metacentric height formula is defined as a method to determine the metacentric height of a floating body, which is the distance between the metacenter and the center of gravity, providing a measure of a ship's stability in water, crucial for safe and efficient navigation in hydrostatic fluid contexts. Metacentric Height is denoted by G_m symbol.

How to evaluate Experimental Determination of Metacentric height using this online evaluator? To use this online evaluator 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.

FAQs on Experimental Determination of Metacentric height

What is the formula to find Experimental Determination of Metacentric height?

The formula of Experimental Determination of Metacentric height is expressed as Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)). Here is an example- 330265.5 = (43.5*38.4)/((43.5+25500)*tan(0.195476876223328)).

How to calculate Experimental Determination of Metacentric height?

With Movable Weight on Ship (W'), Transverse Displacement (x), Ship Weight (W) & Angle of Tilt (Θ) we can find Experimental Determination of Metacentric height using the formula - Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt)). This formula also uses Tangent (tan) function(s).

What are the other ways to Calculate Metacentric Height?

Here are the different ways to Calculate Metacentric Height-

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

Can the Experimental Determination of Metacentric height be negative?

No, the Experimental Determination of Metacentric height, measured in Length cannot be negative.

Which unit is used to measure Experimental Determination of Metacentric height?

Experimental Determination of Metacentric height is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Experimental Determination of Metacentric height can be measured.

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Experimental Determination of Metacentric height Formula

​GoMetacentric Height given Moment of Inertia Formula

​GoMetacentric Height Formula

Experimental Determination of Metacentric height Example

Experimental Determination of Metacentric height Solution

Experimental Determination of Metacentric height Formula Elements

Other Formulas to find Metacentric Height

Other formulas in Hydrostatic Fluid category

How to Evaluate Experimental Determination of Metacentric height?

FAQs on Experimental Determination of Metacentric height

Variable Name

GoMetacentric Height given Moment of Inertia Formula

GoMetacentric Height Formula