Bernoulli's principle

The height (in m) of the liquid in left chamber at $t=500$ s is:

A cylindrical vessel of 40 cm radius is completely filled with water and its capacity is 528 dm³ (dm : decimeter) The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at 70 cm below the top of water level, then horizontal range of water falling on the ground in the beginning is ________ cm.

A liquid of density 600 kg/m³ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is 1.0 cm² and that at $B$ is 20 mm². Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is 10 cm/s. The difference in pressures at $A$ and $B$ points is ________ Pa.

Two large, identical water tanks, 1 and 2, kept on the top of a building of height $H$, are filled with water up to height $h$ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are $t_1$ and $t_2$, respectively. If $H = \left(\dfrac{16}{9}\right)h$, then the ratio $t_1/t_2$ is _____.

Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is _____ $\mathrm{gm\,s^{-1}}$.

An ideal gas of density $\rho = 0.2\ \mathrm{kg\,m^{-3}}$ enters a chimney of height $h$ at the rate of $\alpha = 0.8\ \mathrm{kg\,s^{-1}}$ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is $A_1 = 0.1\ \mathrm m^2$ and the upper end is $A_2 = 0.4\ \mathrm m^2$. The pressure and the temperature of the gas at the lower end are 600 Pa and 300 K, respectively, while its temperature at the upper end is 150 K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take $g = 10\ \mathrm{m\,s^{-2}}$ and the ratio of specific heats of the gas $\gamma = 2$. Ignore atmospheric pressure.

Which of the following statement(s) is(are) correct?

An ideal fluid of density 800 kg m$^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from $a$ to $\dfrac a2$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\dfrac{\sqrt x}6$ ms$^{-1}$ for $x=$ ______. (Given $g=10$ ms$^{-2}$)

The area of cross-section of a large tank is 0.5 m$^2$. It has a narrow opening near the bottom having area of cross-section 1 cm$^2$. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity of the water, coming out of the opening at the time when the height of water level in the tank is 40 cm above the bottom, will be ______ cms$^{-1}$. [Take $g=10$ ms$^{-2}$]

A liquid of density 750 kgm$^{-3}$ flows smoothly through a horizontal pipe that tapers in cross-sectional area from $A_1=1.2\times10^{-2}$m$^2$ to $A_2=\dfrac{A_1}2$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ______ $\times10^{-3}$ m$^3$s$^{-1}$.

Consider a cylindrical tank of radius 1 m is filled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of $5\times10^5$ N is applied an the top surface of water using a piston. The speed of efflux from the hole will be :

(given atmospheric pressure $P_A=1.01\times10^5$ Pa, density of water $\rho_w$ = 1000 kg/m$^3$ and gravitational acceleration g = 10 m/s$^2$)

A train with cross-sectional area $S_t$ is moving with speed $v_t$ inside a long tunnel of cross-sectional area $S_0\ (S_0 = 4S_t)$. 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 $p_0$. If the pressure in the region between the sides of the train and the tunnel walls is $p$, then $p_0 - p = \dfrac{7}{2N}\rho v_t^2$. The value of $N$ is ______.

Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$. Then :

If the density of air is $\rho_a$ and that of the liquid $\rho_\ell$, then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to

A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the lift's motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the list.

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3 m and that of kerosene 2 m. When the hole is opened the velocity of fluid coming out from it is nearly : (take $g=10$ ms$^{-2}$ and density of water $=10^3$ kg m$^{-3}$)

A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius 'a'. The time in which it will be emptied is :

In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of the tube at A and B is 6 mm$^2$ and 10 mm$^2$ respectively. The rate at which water flows through the tube is ($g=10$ ms$^{-2}$)