JEE Advanced 2020 Paper 2

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 betweenthe sides of the train and the tunnel walls is p, then p0−p=

7

2N

ρvt2. The value of N is______.