Angle of heel for metacentric height in experimental method Calculator

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Forces on Submerged Bodies

✖Movable Weight on Floating Vessel is a known weight placed over the center of the vessel floating on the liquid or fluid.ⓘ Movable Weight on Floating Vessel [w₁]			+10% -10%
✖Distance travelled by weight on vessel defines how much path the movable weight has covered onto the floating vessel.ⓘ Distance Travelled by Weight on Vessel [D]			+10% -10%
✖The Weight of Floating Vessel is defined as the weight of the vessel floating onto the fluid including the weight placed over the center of the vessel floating on the liquid or fluid.ⓘ Weight of Floating Vessel [W_fv]			+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 Angle of Heel is the tilted angle of the body in a fluid or liquid.ⓘ Angle of heel for metacentric height in experimental method [θ]

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Formula

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Angle of heel for metacentric height in experimental method

Formula

`"θ" = atan(("w"_{"1"}*"D")/("W"_{"fv"}*"GM"))`

Example

`"8.242093°"=atan(("343N"*"5.8m")/("19620N"*"0.7m"))`

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Angle of heel for metacentric height in experimental method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body))
θ = atan((w₁*D)/(W_fv*GM))
This formula uses 2 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)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Angle of Heel - (Measured in Radian) - The Angle of Heel is the tilted angle of the body in a fluid or liquid.
Movable Weight on Floating Vessel - (Measured in Newton) - Movable Weight on Floating Vessel is a known weight placed over the center of the vessel floating on the liquid or fluid.
Distance Travelled by Weight on Vessel - (Measured in Meter) - Distance travelled by weight on vessel defines how much path the movable weight has covered onto the floating vessel.
Weight of Floating Vessel - (Measured in Newton) - The Weight of Floating Vessel is defined as the weight of the vessel floating onto the fluid including the weight placed over the center of the vessel floating on the liquid or fluid.
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.

STEP 1: Convert Input(s) to Base Unit

Movable Weight on Floating Vessel: 343 Newton --> 343 Newton No Conversion Required
Distance Travelled by Weight on Vessel: 5.8 Meter --> 5.8 Meter No Conversion Required
Weight of Floating Vessel: 19620 Newton --> 19620 Newton No Conversion Required
Metacentric Height of Floating Body: 0.7 Meter --> 0.7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = atan((w₁*D)/(W_fv*GM)) --> atan((343*5.8)/(19620*0.7))

Evaluating ... ...

θ = 0.14385165398971

STEP 3: Convert Result to Output's Unit

0.14385165398971 Radian -->8.24209264958821 Degree (Check conversion here)

FINAL ANSWER

8.24209264958821 ≈ 8.242093 Degree <-- Angle of Heel

(Calculation completed in 00.004 seconds)

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Created by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

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Amrita School of Engineering (ASE), Vallikavu

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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

Angle of heel for metacentric height in experimental method Formula

Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body))
θ = atan((w₁*D)/(W_fv*GM))

What is meta-centre?

It is defined as the point about which a body starts oscillating when the body is tilted by a small angle.

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 Angle of heel for metacentric height in experimental method?

Angle of heel for metacentric height in experimental method calculator uses Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body)) to calculate the Angle of Heel, The Angle of heel for metacentric height in experimental method formula is Known in considering the movable weight (w1) and distance moved by w1 to the metacentric height, weight of the vessel including w1. Angle of Heel is denoted by θ symbol.

How to calculate Angle of heel for metacentric height in experimental method using this online calculator? To use this online calculator for Angle of heel for metacentric height in experimental method, enter Movable Weight on Floating Vessel (w₁), Distance Travelled by Weight on Vessel (D), Weight of Floating Vessel (W_fv) & Metacentric Height of Floating Body (GM) and hit the calculate button. Here is how the Angle of heel for metacentric height in experimental method calculation can be explained with given input values -> 472.2371 = atan((343*5.8)/(19620*0.7)).

FAQ

What is Angle of heel for metacentric height in experimental method?

The Angle of heel for metacentric height in experimental method formula is Known in considering the movable weight (w1) and distance moved by w1 to the metacentric height, weight of the vessel including w1 and is represented as θ = atan((w₁*D)/(W_fv*GM)) or 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 on Floating Vessel is a known weight placed over the center of the vessel floating on the liquid or fluid, Distance travelled by weight on vessel defines how much path the movable weight has covered onto the floating vessel, The Weight of Floating Vessel is defined as the weight of the vessel floating onto the fluid including the weight placed over the center of the vessel floating on the liquid or fluid & 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.

How to calculate Angle of heel for metacentric height in experimental method?

The Angle of heel for metacentric height in experimental method formula is Known in considering the movable weight (w1) and distance moved by w1 to the metacentric height, weight of the vessel including w1 is calculated using Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body)). To calculate Angle of heel for metacentric height in experimental method, you need Movable Weight on Floating Vessel (w₁), Distance Travelled by Weight on Vessel (D), Weight of Floating Vessel (W_fv) & Metacentric Height of Floating Body (GM). With our tool, you need to enter the respective value for Movable Weight on Floating Vessel, Distance Travelled by Weight on Vessel, Weight of Floating Vessel & Metacentric Height of Floating Body 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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