Test if the following equations are dimensionally correct:
A. B.
C. D.
where h = height, S = surface tension, ρ = density, P = pressure,
V = volume, η = coefficient of viscosity, v = frequency and I =
moment of inertia.
A.
Dimensions of h = [L]
Dimensions of S = [MT-2]
Dimensions of ρ = [ML-3]
Dimensions of r = [L]
Dimensions of g = [LT-2]
Checking the R.H.S
Dimensionally
=
= [M0L1T0]
A. is dimensionally correct
B.
Dimensions of v = [LT-1]
Dimensions of P = [ML-1T-2]
Dimensions of ρ = [ML-3]
Checking the R.H.S
Dimensionally
=
B. is dimensionally correct
C.
Dimensions of V = [L3]
Dimensions of P = [ML-1T-2]
Dimensions of r4 = [L4]
Dimensions of t = [T]
Dimensions of l = [L]
Dimensions of η = [ML-1T-1]
Checking the R.H.S
Dimensionally
= =[L3]
C. is dimensionally correct
D.
Dimensions of v = [T-1]
Dimensions of m = [M]
Dimensions of g = [LT-2]
Dimensions of l = [L]
Dimensions of I = [ML2]
Checking the R.H.S
Dimensionally
=
D. is dimensionally correct