MODEL TO PROTOTYPE MULTIPLIER FOR THE VARIABLES COMMONLY USED IN MECHANICS UNDER FROUDE SCALING

GEOMETRY

VARIABLEUNITSCALE FACTORREMARKSLengthLAny characteristic dimension of the objectAreaL22Surface area or projected area on a planeVolumeL33For any portion of the objectAngle None1e.g., between members or solid angle

VARIABLEUNITSCALE FACTORREMARKSRadius of GyrationLMeasured from a fixed pointMoment of Inertia AreaL44Moment of Inertia MassML25Taken about a fixed pointCenter of GravityLMeasured from a reference point

KINEMATICS & DYNAMICS

VARIABLEUNITSCALE FACTORREMARKSTimeT1/2Same reference point (e.g., starting time) is considered as zero timeAccelerationLT-21Rate of change of velocityVelocityLT-11/2Rate of change of displacementDisplacementLPosition at rest is considered as zeroAngular AccelerationT-2-1Rate of change of angular velocityAngular VelocityT-11/2Rate of change of angular displacement

VARIABLEUNITSCALE FACTORREMARKSAngular DisplacementNone1Zero degree is taken as referenceSpring Constant (Linear)MT-22Force per unit length of extensionDamping CoefficientMT-15/2Resistance (viscous) against oscillationDamping FactorNone1Ratio of damping and critical damping coefficientNatural PeriodT1/2Period at which inertia force = restoring force

VARIABLEUNITSCALE FACTORREMARKSMomentumMLT-17/2Mass times linear velocityAngular MomentumML2T-19/2Mass moment of inertia times angular velocityTorqueML2T-24Tangential force times distanceWorkML2T-24Force applied times distance movedPowerML2T-37/2Rate of workImpulseMLT-17/2Constant force times its short duration of timeForce, Thrust, ResistanceMLT-23Action of one body on another to change or tend to change the state of motion of the body acted on

STATICS

VARIABLEUNITSCALE FACTORREMARKSStiffnessML3T-25Modulus of elasticity times the moment of inertia, EIStressML-1T-2Force on an element per unit areaMomentML2T-24Applied force times its from a fixed pointShearMLT-23Force per unit cross sectional area parallel to the forceSection ModulusL33Area moment of inertia divided by the distance from the neural axis to the extreme fiber

HYDRAULICS

VARIABLEUNITSCALE FACTORREMARKSKinetic EnergyML2T-24Capacity of a body for doing work due to its configurationPressure EnergyML2T-24Energy due to pressure headPotential EnergyML2T-24Capacity of a body for doing work due to its configurationFriction LossML2T-24Loss of energy or work due to friction

SCOUR

VARIABLEUNITSCALE FACTORREMARKSParticle DiameterLFor same prototype materialFree Settling VelocityLT-1Final velocity of a freely falling particle in a mediumSediment NumberNone1Nondimensional no. based on velocity and particle sizeShields NumberNone1Nondimensional no. based on velocity and particle size

WAVE MECHANICS

VARIABLEUNITSCALE FACTORREMARKSWave HeightLConsecutive crest to trough distanceWave PeriodTTime between two successive crests passing a pointWave LengthLDistance between two successive crests at a given timeCelerityLT-1Velocity of wave (crest, for example)

VARIABLEUNITSCALE FACTORREMARKSParticle VelocityLT-1Rate of change of movement of a water particleParticle AccelerationLT-21Rate of change of velocity of a water particleParticle OrbitsLPath of a water particle (closed or open)Wave ElevationLForm of wave (distance from still waterline)Wave PressureML-1T-2Force exerted by a water particle per unit areaKeulegan-Carpenter Parameter(v.T/D)None1Dependence of hydrodynamic coefficients on this parameter

STABILITY

VARIABLEUNITSCALE FACTORREMARKSDisplacement (Volume)L33Volume of water moved by a submerged object (or part therof)Righting & Overturning Moment (Hard Volume)ML2T-24Moment about a fixed point of a displaced weight and dead weight, respectivelyNatural PeriodTPeriod of free oscillation in still water due to an initial disturbanceMetacenterLInstantaneous center of rotationCenter of BuoyancyLDistance of C.G. of displaced volume from a fixed pointSoft VolumeL33Volume of trapped air in a memberBuoyancy Pickup per Unit AngleL33Increase in displaced volume per unit tilt angle

MATERIAL PROPERTIES

VARIABLEUNITSCALE FACTORREMARKSDensityML-31Mass per unit volumeModulus of ElasticityML-1T-2Ratio of tensile or compressive stress to strainModulus of RigidityML-1T-2Ratio of shearing stress to strain