Taking frequency f velocity v and density row to be the fundamental quantities then the dialenntional foemula is
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Dimension of frequency , F = [T⁻¹]
Dimension of velocity ,V = [LT⁻¹]
Dimension of density , D = [ML⁻³]
Dimension of momentum , P = [MLT⁻¹]
Let relation between P with F, V and D is given by
P = FᵃVᵇDˣ
[MLT⁻¹] = [T⁻¹]ᵃ[LT⁻¹]ᵇ[ML⁻³]ˣ
[MLT⁻¹] = [Mˣ][Lᵇ⁻³ˣ][T⁻ᵃ⁻ᵇ]
Compare both sides,
x = 1 , b - 3x = 1 and -a - b = -1
b = 3x + 1 = 4
a = 1 - b = -3
Hence, P = F⁻³V⁴D¹
Dimension of velocity ,V = [LT⁻¹]
Dimension of density , D = [ML⁻³]
Dimension of momentum , P = [MLT⁻¹]
Let relation between P with F, V and D is given by
P = FᵃVᵇDˣ
[MLT⁻¹] = [T⁻¹]ᵃ[LT⁻¹]ᵇ[ML⁻³]ˣ
[MLT⁻¹] = [Mˣ][Lᵇ⁻³ˣ][T⁻ᵃ⁻ᵇ]
Compare both sides,
x = 1 , b - 3x = 1 and -a - b = -1
b = 3x + 1 = 4
a = 1 - b = -3
Hence, P = F⁻³V⁴D¹
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