Young-Laplace law states that the excess pressure inside a soap bubble of radius R is given by AP = 4σ / R, where a is the coefficient of surface tension of the soap. The EOTVOS number E0 is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of g, the acceleration due to gravity ρ the density of the surround in g fluid ρ and a characteristic length scale L4 which could be the radius of the bubble. A possible expression for E0 is

Question

Young-Laplace law states that the excess pressure inside a soap bubble of radius R is given by AP = 4σ / R, where a is the coefficient of surface tension of the soap. The EOTVOS number E0 is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of g, the acceleration due to gravity ρ the density of the surround in g fluid ρ and a characteristic length scale L4 which could be the radius of the bubble. A possible expression for E0 is (A) (ρ g/σ L3) (B) (ρ L2/σ g) (C) (ρ gL2/σ) (D) (gL2/σρ)

Tardigrade Admin · Accepted Answer

As EOTVOS number E0 is dimensionless, we check dimensions of options given to the choose correct answer. Now [(ρ gL2/σ)]=([ρ].[g].[L]2/[σ]) =([ML-3][LT-2].[L]2/[ML-2]) =[m0L0T0]= Dimensionless

$\frac{ρ g}{σ L ^{3}}$

$\frac{ρ L ^{2}}{σ g}$

$\frac{ρ g L ^{2}}{σ}$

$\frac{g L ^{2}}{σ ρ}$

As $EOT V OS$ number $E_{0}$ is dimensionless, we check dimensions of options given to the choose correct answer.
Now $[\frac{ρ g L ^{2}}{σ}] = \frac{[ ρ ] . [ g ] . [ L ] ^{2}}{[ σ ]}$
$= \frac{[ M L ^{- 3} ] [ L T ^{- 2} ] . [ L ] ^{2}}{[ M L ^{- 2} ]}$
$= [m^{0} L^{0} T^{0}] =$ Dimensionless

σL3ρg​

σgρL2​

σρgL2​