Similarity Law between Centrifuge Scale Test and Prototype Underwater Explosion

Table 2

Scaling similarity relation of dynamic parameters of underwater explosion [29].

Parameters	Dimension	Prototype	Scale model	Value
Explosive radius	L	R0	λR0	λ
Standoff distance		R	λR	λ
Explosion depth		D	λD	λ
Bubble radius		Rb	λRb	λ
Length		L	λL	λ
Displacement		L	λL	λ
Period	T	Tb	λTb	λ
Explosion weight	M	W	λ^3W	λ^3
Structure weight		M	λ^3M	λ^3
Water density	ML^−3			1
Explosion density		ρc	ρc	1
Fluid velocity	LT^−1			1
Detonation velocity		Uc	Uc	1
Atmosphere pressure	ML^−1T^−2	Patm	Patm	1
Shock wave peak pressure		Pm	Pm	1
Bubble pulsation pressure		Pbm	Pbm	1
Hydrostatic pressure		P0	P0	1
Strength		σmax	σmax	1
Surface load		P	P	1
Stress		σ = σmax	σ = σmax	1
Stress-strain relationship		f = σ (ε)	f = σ (ε)	1
Strain	1	ε	ε	1
Acceleration	LT^−2		/λ	1/λ