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Mechanical Properties of Fluids

Bernoulli's equation

A train with cross-sectional area S_{t} is moving with speed v

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A train with cross-sectional area $S_{t}$ is moving with speed $v_{0}$ 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 between its sides and the walls of the tunnel. Also, the air flow 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 $p$ then $p_{0} - p = \frac{7}{2 N} ρ v_{t}^{2}$ . The value of $N$ is

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Updated on: Apr 25, 2023

Exam:

JEE Advanced 2020

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Elijah Discussed

A train with cross-sectional area

S_{t}

is moving with speed

v_{0}

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 between its sides and the walls of the tunnel. Also, the air flow 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

p

then

p_{0} - p = \frac{7}{2 N} ρ v_{t}^{2}

. The value of

N

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Applying Bernoulli's equation,

p_{0} + \frac{1}{2} ρ v_{1}^{2} = p + \frac{1}{2} ρ v^{2} p_{0} - p = \frac{1}{2} ρ (v^{2} - v_{1}^{2})

From equation of continuity,

4 S_{t} v_{t} = v \times 3 S_{l} \Rightarrow v = \frac{4}{3} v_{t}

From Eqs. (i) and (ii), we get

p_{0} - p = \frac{1}{2} ρ (\frac{16}{9} v_{t}^{2} - v_{t}^{2}) = \frac{1}{2} ρ \frac{7 v _{t}^{2}}{9} ∴ N = 9

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Question Text	A train with cross-sectional area $S_{t}$ is moving with speed $v_{0}$ 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 between its sides and the walls of the tunnel. Also, the air flow 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 $p$ then $p_{0} - p = \frac{7}{2 N} ρ v_{t}^{2}$ . The value of $N$ is
Updated On	Apr 25, 2023
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 7
Upvotes	780
Avg. Video Duration	7 min

Text solutionVerified

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