Volume of Liquid Displaced given Metacentric Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G)
VD = Iwl/(GM+BG)
This formula uses 4 Variables
Variables Used
Volume of Liquid Displaced by Body - (Measured in Cubic Meter) - Volume of Liquid displaced by Body is the total volume of the liquid which is displaced the immersed/floating body.
Moment of Inertia of Waterline Area - (Measured in Kilogram Square Meter) - Moment of inertia of waterline area at a free surface of floating-level about an axis passing through the center of area.
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 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
Moment of Inertia of Waterline Area: 100 Kilogram Square Meter --> 100 Kilogram Square Meter No Conversion Required
Metacentric Height: 33000 Millimeter --> 33 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
VD = Iwl/(GM+BG) --> 100/(33+1.5)
Evaluating ... ...
VD = 2.89855072463768
STEP 3: Convert Result to Output's Unit
2.89855072463768 Cubic Meter --> No Conversion Required
FINAL ANSWER
2.89855072463768 2.898551 Cubic Meter <-- Volume of Liquid Displaced by Body
(Calculation completed in 00.020 seconds)

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Osmania University (OU), Hyderabad
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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

Volume of Liquid Displaced given Metacentric Height Formula

Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G)
VD = Iwl/(GM+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 Volume of Liquid Displaced given Metacentric Height?

Volume of Liquid Displaced given Metacentric Height calculator uses Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G) to calculate the Volume of Liquid Displaced by Body, The Volume of Liquid Displaced given Metacentric Height formula is defined as the volume of the liquid displaced when the object is submerged. Volume of Liquid Displaced by Body is denoted by VD symbol.

How to calculate Volume of Liquid Displaced given Metacentric Height using this online calculator? To use this online calculator for Volume of Liquid Displaced given Metacentric Height, enter Moment of Inertia of Waterline Area (Iwl), Metacentric Height (GM) & Distance Between Point B and G (BG) and hit the calculate button. Here is how the Volume of Liquid Displaced given Metacentric Height calculation can be explained with given input values -> 60.60606 = 100/(33+1.5).

FAQ

What is Volume of Liquid Displaced given Metacentric Height?
The Volume of Liquid Displaced given Metacentric Height formula is defined as the volume of the liquid displaced when the object is submerged and is represented as VD = Iwl/(GM+BG) or Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G). Moment of inertia of waterline area at a free surface of floating-level about an axis passing through the center of area, 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 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 Volume of Liquid Displaced given Metacentric Height?
The Volume of Liquid Displaced given Metacentric Height formula is defined as the volume of the liquid displaced when the object is submerged is calculated using Volume of Liquid Displaced by Body = Moment of Inertia of Waterline Area/(Metacentric Height+Distance Between Point B and G). To calculate Volume of Liquid Displaced given Metacentric Height, you need Moment of Inertia of Waterline Area (Iwl), Metacentric Height (GM) & Distance Between Point B and G (BG). With our tool, you need to enter the respective value for Moment of Inertia of Waterline Area, Metacentric Height & 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.
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