A train with cross sectional area st is moving with a speed vt inside a long tunnel of cross sectional area assume that all the air in front of the train
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Answer:
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The complete question will be:
The complete question will be:A train with cross-sectional area St is moving with speed vt inside a long tunnel of cross-sectional area S0 (S0 = 4St). 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 p0. If the pressure in the region between the sides of the train and the tunnel walls is p, then p0- p = 7/2Npvt^2. The value of N is ?
Given:
Cross sectional area of train = St
Cross sectional area of tunnel S0= 4St
Ambient pressure and pressure inside the train = p0
Pressure between the sides of the train and the tunnel wall= p
p0-p = 7/2Np(vt^2)
To find:
The value of N
Solution:
Applying Bernoulli's equation, we get:
p0+ 1/2 pv^2 = p 1/2pvt^2
p0-p = 1/2p(vt^2 - v^2)
From the equation of continuity
Also, 4 Stvt= v* 3St
v= 4/3 vt
From 1 and 2 equation:
p0-p = 1/2 p(16/9vt^2 - vt^2) = 1/2p7/9 vt^2
Since p0-p= 7/2Np(vt^2)
7/2Np(vt^2) = 1/2p7/9 vt^2
On solving we get N=9
