A light cylindrical vessel which is kept on a frictional horizontal surface, its base area A and height H. A hole of cross –sectional area ‘a’ is made at a height $\frac{H}{4}$ from it’s base (bottom).Then choose correct option/s.

A train with cross-sectional area S_t is moving with speed 𝑣_𝑡 inside a long tunnel of cross-sectional area S₀ (S₀ = 4S_t). Assume that almost all the air (density $\rho$) 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 ${\mathrm{p}}_0-\mathrm{p}=\frac{7}{2\mathrm{N}}\rho {\mathrm{v}}_{\mathrm{t}}^2$. The value of N is_________