Question

Test if the following equation are dimensionally correct (S = surface tension ρ= density P = pressure v = volume n = coefficient of viscocity r = redious)

Answer 1

(d) all correct

Explanation:

 (1)

h = [(2s cosθ) / (ρrg)]

s = surface tension = [M][T^–2] = [(Force) / (length)]

 ρ = density = [(mass) / (volume)] = [M¹][L^–3]

 r = radius = [L]

 g = acceleration = [L][T^–2]

 ∴ [(2s cosθ) / (rρg)]

 i.e.      [S / (rρg)] = {([M][T^–2]) / ([L][M¹][L^–3][L][T^–2])} = [L]

 h = height = [L]

hence formula correct

 (2)

 velocity = [L¹T^–1]

Pressure = [(Force) / (area)] = ([M¹L¹T^–2] / [L²]) = [M¹L^–1T^–2]

 density = [(mass) / (volume)] = [M¹L^–3].

 hence √[(pressure) / (density)] = √([M¹L¹T^–2] / [M¹L^–3]) = [LT^–1]

 hence formula is correct

 (3)

 volume = [L³]

[(πpr⁴t) / (8ηℓ)] i.e. [(pr⁴t) / (ηℓ)] = {([M¹L^–1T^–2] [L⁴][T]) / ([M¹L^–1T^–1][L])} = [L³]

because

p = pressure = [(Force) / (area)] = [M¹L^–1T^–2]

η = coefficient of viscosity = [M¹L^–1T^–1].

  hence formula is correct.