Metacentric Height given Time Period of Rolling Calculator

✖The Radius of Gyration or gyradius 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.ⓘ Radius of Gyration [K_g]			+10% -10%
✖Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.ⓘ Time Period of Rolling [T_r]			+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 Time Period of Rolling [H_metacentric]

⎘ Copy

👎

Formula

✖

Metacentric Height given Time Period of Rolling

Formula

`"H"_{"metacentric"} = (("K"_{"g"}*pi)^2)/(("T"_{"r"}/2)^2*"[g]")`

Example

`"0.730432m"=(("4.43m"*pi)^2)/(("10.4s"/2)^2*"[g]")`

Calculator

LaTeX

Reset

👍

Download Fluid in Motion Formulas PDF

Metacentric Height given Time Period of Rolling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g])
H_metacentric = ((K_g*pi)^2)/((T_r/2)^2*[g])
This formula uses 2 Constants, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius 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.
Time Period of Rolling - (Measured in Second) - Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration: 4.43 Meter --> 4.43 Meter No Conversion Required
Time Period of Rolling: 10.4 Second --> 10.4 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_metacentric = ((K_g*pi)^2)/((T_r/2)^2*[g]) --> ((4.43*pi)^2)/((10.4/2)^2*[g])

Evaluating ... ...

H_metacentric = 0.730432073561462

STEP 3: Convert Result to Output's Unit

0.730432073561462 Meter --> No Conversion Required

FINAL ANSWER

0.730432073561462 ≈ 0.730432 Meter <-- Metacentric Height

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Fluid Mechanics » Fluid in Motion » Hydrodynamics Basics » Metacentric Height given Time Period of Rolling

Credits

Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has verified this Calculator and 1900+ more calculators!

< 9 Hydrodynamics Basics Calculators

Moment of Momentum Equation

Go Torque Exerted on Wheel = Density of Liquid*Discharge*(Velocity at Section 1-1*Radius of Curvature at Section 1-Velocity at Section 2-2*Radius of Curvature at Section 2)

Poiseuille's Formula

Go Volumetric Flow Rate of Feed to Reactor = Pressure Changes*pi/8*(Pipe Radius^4)/(Dynamic Viscosity*Length)

Power Developed by Turbine

Go Power Developed by Turbine = Density of Liquid*Discharge*Velocity of Whirl at Inlet*Tangential Velocity at Inlet

Metacentric Height given Time Period of Rolling

Go Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g])

Reynolds Number

Go Reynolds Number = (Density of Liquid*Fluid Velocity*Pipe Diameter)/Dynamic Viscosity

Reynolds Number given Length

Go Reynolds Number = Density of Liquid*Velocity*Length/Kinematic Viscosity

Power Required to Overcome Frictional Resistance in Laminar Flow

Go Power Generated = Specific Weight of Liquid 1*Rate of Flow of Fluid*Head Loss

Power

Go Power Generated = Force on Fluid Element*Change in Velocity

Reynolds Number given Frictional Factor of Laminar Flow

Go Reynolds Number = 64/Friction Factor

Metacentric Height given Time Period of Rolling Formula

Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g])
H_metacentric = ((K_g*pi)^2)/((T_r/2)^2*[g])

What is Timeperiod?

The time period is the time taken by a complete cycle of the wave to pass a point, Frequency is the number of complete cycle of waves passing a point in unit time. Frequency and time period are in a reciprocal relationship that can be expressed mathematically as T = 1/f or as f = 1/T.

How to Calculate Metacentric Height given Time Period of Rolling?

Metacentric Height given Time Period of Rolling calculator uses Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]) to calculate 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_metacentric symbol.

How to calculate Metacentric Height given Time Period of Rolling using this online calculator? To use this online calculator 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. Here is how the Metacentric Height given Time Period of Rolling calculation can be explained with given input values -> 0.730432 = ((4.43*pi)^2)/((10.4/2)^2*[g]).

FAQ

What is Metacentric Height given Time Period of Rolling?

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 and is represented as H_metacentric = ((K_g*pi)^2)/((T_r/2)^2*[g]) or Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]). The Radius of Gyration or gyradius 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 & Time Period of Rolling is the time taken by an object to return to its upright position while it is rolling.

How to calculate Metacentric Height given Time Period of Rolling?

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 is calculated using Metacentric Height = ((Radius of Gyration*pi)^2)/((Time Period of Rolling/2)^2*[g]). To calculate Metacentric Height given Time Period of Rolling, you need Radius of Gyration (K_g) & Time Period of Rolling (T_r). With our tool, you need to enter the respective value for Radius of Gyration & Time Period of Rolling and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search