A fluid of density ' ρ ' is flowing through a uniform tube of diameter ' d '. The coefficient of viscosity of the fluid is ' η ', then critical velocity of the fluid is (a) inversely proportional to ' η ' (b) directly proportional to ' η ' (c) directly proportional to ' d ' (d) directly proportional to ' ρ '

Answer: (b). Rn = (ρ vc d)/(η) ⇒ vc = (Rn η)/(ρ d) vc ∝ η, and vc ∝ 1/ρ, vc ∝ 1/d. So the answer is (b) directly proportional to η.

A fluid of density ' ρ ' is flowing through a uniform tube of… | MHT CET 2023 (11 May, Shift 2)

Q9MHT CET 2023 · 11 MAY · SHIFT 2Easy

Types of Flow, Reynolds Number & Continuity

A fluid of density ' $\rho$ ' is flowing through a uniform tube of diameter ' $d$ '. The coefficient of viscosity of the fluid is ' $\eta$ ', then critical velocity of the fluid is

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Answer: (b)

$R_n = \dfrac{\rho v_c d}{\eta} \Rightarrow v_c = \dfrac{R_n \eta}{\rho d}$
$v_c \propto \eta$ , and $v_c \propto 1/\rho$ , $v_c \propto 1/d$ .
So the answer is (b) directly proportional to $\eta$ .

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