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Metacentric Height given Time Period of Rolling 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

H m = \frac{{(K g \cdot π)}^{2}}{{(\frac{T r}{2})}^{2} \cdot [g]}

H_m - Metacentric Height?K_g - Radius of Gyration?T_r - Time Period of Rolling?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Metacentric Height given Time Period of Rolling Example

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Here is how the Metacentric Height given Time Period of Rolling equation looks like with Values.

Here is how the Metacentric Height given Time Period of Rolling equation looks like with Units.

Here is how the Metacentric Height given Time Period of Rolling equation looks like.

0.7304 = \frac{{(4.43 \cdot 3.1416)}^{2}}{{(\frac{10.4}{2})}^{2} \cdot 9.8066}

0.7304m = \frac{{(4.43m \cdot 3.1416)}^{2}}{{(\frac{10.4s}{2})}^{2} \cdot 9.8066m/s²}

0.7304 = \frac{{(4.43 \cdot 3.1416)}^{2}}{{(\frac{10.4}{2})}^{2} \cdot 9.8066}

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Metacentric Height given Time Period of Rolling Solution

Follow our step by step solution on how to calculate Metacentric Height given Time Period of Rolling?

FIRST Step Consider the formula

H m = \frac{{(K g \cdot π)}^{2}}{{(\frac{T r}{2})}^{2} \cdot [g]}

Next Step Substitute values of Variables

∴

H m = \frac{{(4.43m \cdot π)}^{2}}{{(\frac{10.4s}{2})}^{2} \cdot [g]}

Next Step Substitute values of Constants

∴

H m = \frac{{(4.43m \cdot 3.1416)}^{2}}{{(\frac{10.4s}{2})}^{2} \cdot 9.8066m/s²}

Next Step Prepare to Evaluate

∴

H m = \frac{{(4.43 \cdot 3.1416)}^{2}}{{(\frac{10.4}{2})}^{2} \cdot 9.8066}

Next Step Evaluate

∴

H m = 0.730432073561462m

LAST Step Rounding Answer

∴

H m = 0.7304m

Metacentric Height given Time Period of Rolling Formula Elements

Variables

Constants

Metacentric Height

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

Symbol: H_m

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Metacentric Height

Radius of Gyration

The Radius of Gyration is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.

Symbol: K_g

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Gyration

Time Period of Rolling

Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

Symbol: T_r

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Period of Rolling

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Hydrodynamics Basics category

Go Moment of Momentum Equation

T = ρ 1 \cdot Q \cdot (v 1 \cdot R 1 - v 2 \cdot R 2)

Go Poiseuille's Formula

Q v = Δp \cdot \frac{π}{8} \cdot \frac{{r p}^{4}}{μ v \cdot L}

Go Power

P w = F e \cdot Δv

Go Power Developed by Turbine

P T = ρ 1 \cdot Q \cdot V wi \cdot ν t

How to Evaluate Metacentric Height given Time Period of Rolling?

Metacentric Height given Time Period of Rolling evaluator uses Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]) to evaluate the Metacentric Height, The Metacentric Height given Time Period of Rolling formula is a measurement of the initial static stability of a floating body. It is calculated as the distance between the center of gravity of a ship and its metacenter. Metacentric Height is denoted by H_m symbol.

How to evaluate Metacentric Height given Time Period of Rolling using this online evaluator? To use this online evaluator for Metacentric Height given Time Period of Rolling, enter Radius of Gyration (K_g) & Time Period of Rolling (T_r) and hit the calculate button.

FAQs on Metacentric Height given Time Period of Rolling

What is the formula to find Metacentric Height given Time Period of Rolling?

The formula of Metacentric Height given Time Period of Rolling is expressed as Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]). Here is an example- 0.730432 = ((4.43*pi)^2)/((10.4/2)^2*[g]).

How to calculate Metacentric Height given Time Period of Rolling?

With Radius of Gyration (K_g) & Time Period of Rolling (T_r) we can find Metacentric Height given Time Period of Rolling using the formula - Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]). This formula also uses Gravitational acceleration on Earth, Archimedes' constant .

Can the Metacentric Height given Time Period of Rolling be negative?

No, the Metacentric Height given Time Period of Rolling, measured in Length cannot be negative.

Which unit is used to measure Metacentric Height given Time Period of Rolling?

Metacentric Height given Time Period of Rolling is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Metacentric Height given Time Period of Rolling can be measured.

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