Continuity equation

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

A water spray gun is attached to a hose of cross sectional area 30 cm². The gun comprises of 10 perforations each of cross sectional area of 15 mm². If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

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$^{-2}$)

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$^{-1}$.

A pressure-pump has a horizontal tube of cross sectional area 10 cm$^2$ for the outflow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is :

[given: density of water = 1000 kg/m$^3$]

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 it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\dfrac2{\sqrt\pi}$ cm then the Reynolds number for the flow is (density of water = $10^3$ kg/m$^3$ and viscosity of water = $10^{-3}$ Pa.s) close to :

If the piston is pushed at a speed of $5\ \mathrm{mm\,s^{-1}}$, the air comes out of the nozzle with a speed of

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

Water is flowing at a speed of 1.5 ms$^{-1}$ through a horizontal tube of cross-sectional area $10^{-2}$ m$^2$ and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water $=10^3$ kgm$^{-3}$).

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$^{-2}$)

STATEMENT-1: The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT-2: In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.