A train with cross-sectional area S _ t is moving with speed v _ t inside a long tunnel of cross-sectional area S _ 0 ( S _ 0 = 4 S _ t ). Assume that almost all the air (density ρ ) in front of the train flows back

Correct answer: 0 4 S _ t v _ t = (3 S _ t )v ⇒ v = (4)/(3) v _ t Apply Bernoulli's theorem, P _ 0 + (1)/(2)ρ v _ t ^ 2 = P + (1)/(2)ρ ((4)/(3) v _ t ) ^ 2 P _ 0 - P = (7)/(18)ρ v _ t ^ 2 ⇒ N = 9

JEE Advanced 2020Paper 2

Exam: JEE Advanced
Year: 2020
Paper: Paper 2
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Advanced 2020 · Paper 2 · Physics · Mechanical Properties of Fluids

A train with cross-sectional area S _ t is moving with speed v _ t...

A train with cross-sectional area

{S}_{t}

is moving with speed

{v}_{t}

inside a long tunnel of cross-sectional area

{S}_{0}\left({S}_{0} = 4{S}_{t}\right). Assume that almost all the air (density

) in front of the train flows back between its sides and the walls of the tunnel. Also, the airflow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be

{P}_{0}

. If the pressure in the region between the sides of the train and the tunnel walls is

, then \left({P}_{0} - P\right) = \dfrac{7}{2N}

ρ{v}_{t}^{2} .

The value of

is _______.

A train with cross-sectional area S _ t is moving with speed v _ t inside a long tunnel of cross-sectional area S _ 0 (

Correct answer

Step-by-step solution

A train with cross-sectional area S _ t is moving with speed v _ t inside a long tunnel of cross-sectional area S _ 0 (

$4{S}_{t}{v}_{t} = \left(3{S}_{t}\right)v$

$⇒ v = \dfrac{4}{3}{v}_{t}$

Apply Bernoulli's theorem,

${P}_{0} + \dfrac{1}{2}ρ{v}_{t}^{2} = P + \dfrac{1}{2}ρ{\left(\dfrac{4}{3}{v}_{t}\right)}^{2}$

${P}_{0} - P = \dfrac{7}{18}ρ{v}_{t}^{2}$

$⇒ N = 9$

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