A train of cross-sectional area Sₜ moves at speed vₜ in a tunnel of area S₀ = 4Sₜ. Nearly all air in front flows backward through the annular space. If p₀−p = (7/(2N))ρvₜ², find N.
Physics · Fluid Mechanics
JEE Advanced 2020

Question

A train of cross-sectional area Sₜ moves at speed vₜ in a tunnel of area S₀ = 4Sₜ. Nearly all air in front flows backward through the annular space. If p₀−p = (7/(2N))ρvₜ², find N.

G1 Physics · Accepted Answer

Step 1: Use continuity A₁v₁ = A₂v₂ and Bernoulli's equation P + ½ρv² + ρgh = constant; for jets use momentum flux ṁΔv. Step 2: Substitute the stated areas, levels and pressures, including Torricelli v = √(2gh) where applicable. Applying these relations to the given data gives 9. Final answer: 9.