Metacentric Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Metacentric Height = Distance between Point B and M-Distance Between Point B and G
GM = BM-BG
This formula uses 3 Variables
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.
Distance between Point B and M - (Measured in Meter) - Distance between Point B and M is defined as the vertical distance between the center of buoyancy of the body and the metacenter of that body. Where B stands for buoyancy and M stands for metacenter.
Distance Between Point B and G - (Measured in Meter) - Distance between Point B and G is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.
STEP 1: Convert Input(s) to Base Unit
Distance between Point B and M: 52 Millimeter --> 0.052 Meter (Check conversion here)
Distance Between Point B and G: 1500 Millimeter --> 1.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
GM = BM-BG --> 0.052-1.5
Evaluating ... ...
GM = -1.448
STEP 3: Convert Result to Output's Unit
-1.448 Meter -->-1448 Millimeter (Check conversion here)
FINAL ANSWER
-1448 Millimeter <-- Metacentric Height
(Calculation completed in 00.004 seconds)

Credits

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19 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)
Surface Energy given Surface Tension
Go Surface Energy = Surface Tension*Surface Area
Surface Area given Surface Tension
Go Surface Area = Surface Energy/Surface Tension

Metacentric Height Formula

Metacentric Height = Distance between Point B and M-Distance Between Point B and G
GM = BM-BG

What is metacentric height?

The vertical distance between G and M is referred to as the metacentric height. The relative positions of vertical centre of gravity G and the initial metacentre M are extremely important with regard to their effect on the ship's stability.

How to Calculate Metacentric Height?

Metacentric Height calculator uses Metacentric Height = Distance between Point B and M-Distance Between Point B and G to calculate the Metacentric Height, Metacentric Height is defined as the vertical distance between the center of gravity of the body and the metacenter of that body. Metacentric Height is denoted by GM symbol.

How to calculate Metacentric Height using this online calculator? To use this online calculator for Metacentric Height, enter Distance between Point B and M (BM) & Distance Between Point B and G (BG) and hit the calculate button. Here is how the Metacentric Height calculation can be explained with given input values -> -1448000 = 0.052-1.5.

FAQ

What is Metacentric Height?
Metacentric Height is defined as the vertical distance between the center of gravity of the body and the metacenter of that body and is represented as GM = BM-BG or Metacentric Height = Distance between Point B and M-Distance Between Point B and G. Distance between Point B and M is defined as the vertical distance between the center of buoyancy of the body and the metacenter of that body. Where B stands for buoyancy and M stands for metacenter & Distance between Point B and G is the vertical distance between the center of buoyance of the body and center of gravity.where B stands for center of buoyancy and G stands for center of gravity.
How to calculate Metacentric Height?
Metacentric Height is defined as the vertical distance between the center of gravity of the body and the metacenter of that body is calculated using Metacentric Height = Distance between Point B and M-Distance Between Point B and G. To calculate Metacentric Height, you need Distance between Point B and M (BM) & Distance Between Point B and G (BG). With our tool, you need to enter the respective value for Distance between Point B and M & Distance Between Point B and G 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 Distance between Point B and M & Distance Between Point B and G. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Metacentric Height = (Movable Weight on Ship*Transverse Displacement)/((Movable Weight on Ship+Ship Weight)*tan(Angle of Tilt))
  • Metacentric Height = Moment of Inertia of Waterline Area/Volume of Liquid Displaced by Body-Distance Between Point B and G
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