Question

Assuming that the Critical Velocity of Viscous Liquid is flowing through a Capillary Tube depends on Radius r of tube, Density p, and Coefficient of Viscosity of the liquid, Find Expression for critical velocity.​

Answer 1

Answer :-

V = kη/r²ρ

Explanation :-

According to the question, Critical Velocity  of viscous liquid is flowing through a capillary tube depends on radius r of tube , density p,and coefficient of viscosity of the liquid.

Let the critical velocity is proportional to rᵃ,  ρᵇ , ηⁿ.

Then,

V = krᵃ,  ρᵇ , ηⁿ, k is any dimension less constant.

Thus,

• Dimension of V = LT⁻¹
• Dimension of r = L
• Dimension of ρ = ML⁻³
• Dimension of η = ML⁻¹T⁻¹

Now, Putting dimension on both sides of equation,

[LT⁻¹] = [L]ᵃ[ML⁻³]ᵇ[ML⁻¹T⁻¹]ⁿ

[M°LT⁻¹] = [Mᵇ⁺ⁿ][Lᵃ⁻ⁿ⁻³ᵇ][T⁻ⁿ]

On comparing,

n = 1, a - n - 3b = 1 and b + n = 0

b = -n = -1

Now, in a - n - 3b =1,

a - 1 - 3(-1) = 1

a + 2 = 1

a = -1

Thus, V = kη/r²ρ

This will be the relation. Now, k is constant. Its value was determined by Physicist 'Reynolds' and hence called as Reynolds Number.

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