A train with cross-sectional area $S _{ t }$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S _0\left( S _0=4 S _{ t }\right)$. 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 $p _0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$, then $p _0- p =\frac{7}{2 N } \rho v_{ t }^2$. The value of $N$ is. . . . .
IIT 2020, Advanced
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionA vessel containing water is moving with a constant speed towards right along a straight horizontal path. if the vessel is given a constant retardation towards the right along a straight line, which of the above diagram represents the surface of the liquid?
- 2An air bubble of volume $1\,cm ^3$ rises from the bottom of a lake $40\,m$ deep to the surface at a temperature of $12^{\circ}\,C$. The atmospheric pressure is $1 \times 10^5 Pa$, the density of water is $1000\,kg / m ^3$ and $g =10\,m / s ^2$. There is no difference of the temperature of water at the depth of $40\,m$ and on the surface. The volume of air bubble when it reaches the surface will be $..........\,cm^{3}$View Solution
- 3A highly viscous liquid of viscosity coefficient $\eta$ flows through a fixed horiwntal cylindrical tube (fixed from outer surface) of internal radius $r$, thickness $t (t << r)$ and length $l$. Volume of liquid flowing per;second is $Q$ and pressure difference across the tube is $P$. Modulus of rigidity of material of tube is $\beta$. Shear strain in the tube will beView Solution
- 4A large tank is filled with water (density $=$ $10^3 $ $kg/m^3$).A small hole is made at a depth $10$ $m$ below water surface. The range of water issuing out of the hole is Ron ground. What extra pressure must be applied on the water surface so that the range becomes $2R $ (take $1$ $atm$ $=$ $10^5$ $Pa$ and $g$ $=$ $10$ $m/s^2):$ ...... $atm$View Solution
- 5Given below are two statements:View Solution
Statement $I :$ Pressure in a reservoir of water is same at all points at the same level of water.
Statement $II :$ The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below:
- 6The diameter of an air bubble which was initially $2\,mm$, rises steadily through a solution of density $1750\,kg\,m\,m ^{-3}$ at the rate of $0.35\,cms ^{-1}$. The coefficient of viscosity of the solution is poise (in nearest integer). (the density of air is negligible).View Solution
- 7Water is flowing with a velocity of $2\,m/s$ in a horizontal pipe where cross-sectional area is $2 \times 10^{-2}\, m^2$ at pressure $4 \times 10^4\, pascal$. The pressure at cross-section of area $0.01\, m^2$ in pascal will beView Solution
- 8A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $(v)$ as a function of time $(t)$ isView Solution
- 9View SolutionWater containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region, the bubbles
- 10View SolutionThe weight of an aeroplane flying in the air is balanced by