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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=72Nρvt2. The value of N is_________

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answer is 9.

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Detailed Solution

Applying Bernoulli's equationP0+12ρvt2=P+12ρv2P0−P=12ρv2−vt2….. (i) From equation of continuity Also, 4Stvt=v×3St⇒v=43vt … (ii)  From (i) and (ii) P0−P=12ρ169vt2−vt2=12ρ7vt29∴N=9
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A train with cross-sectional area St is moving with speed 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=72Nρvt2. The value of N is_________