JEE Fluid Mechanics PYQs with Video Solutions, Download PDF

A soap bubble of surface tension 0.04 N/m is blown to a diameter of 7 cm. If (15000 - x) $$\mu J$$ of work is done in blowing it further to make its diameterl4 cm, then the value of x is_____.
$$\left(\pi=22/7\right)$$

The amount of work done to break a big water drop of radius  $$' R '$$  into  27  small drops of equal radius is  $$10\,J.$$ The work done required to break the same big drop into  64  small drops of equal radius will be:

Small water droplets of radius 0.01 mm are formed in the upper atmosphere and falling with a terminal velocity of 10 cm/s. Due to condensation, if 8 such droplets are coalesced and formed a larger drop, the new terminal velocity will be _____ cm/s.

A bubble has surface tension $$S$$. The ideal gas inside the bubble has ratio of specific heats $$\gamma = \dfrac{5}{3}$$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $$P_{a1}$$, the radius of the bubble is found to be $$r_1$$ and the temperature of the enclosed gas is $$T_1$$. When the atmospheric pressure is $$P_{a2}$$, the radius of the bubble and the temperature of the enclosed gas are $$r_2$$ and $$T_2$$, respectively.

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

In an experiment to verify Stokes law, a small spherical ball of radius $$r$$ and density $$\rho$$ falls under gravity through a distance $$h$$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $$h$$ is proportional to: (ignore viscosity of air)

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of: (density of water = 100 kg/m$$^{3}$$, coefficient of viscosity of water = 1 mPa s)

A tub is filled with water and a wooden cube 10 cm × 10 cm × 10 cm is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by 3.87 cm. The mass of the metal coin is __________ gram. (Take water density as 1 g/cm$$^3$$ and density of wood = 0.4 g/cm$$^3$$)

A hollow spherical shell at outer radius $$R$$ floats just submerged under the water surface. The inner radius of the shell is $$r$$. If the specific gravity of the shell material is $$\frac{27}{8}$$ with respect to water, the value of $$r$$ is:

A square hole of side length $$\ell$$ is made at a depth of $$h$$ and a circular hole of radius $$r$$ is made at a depth of $$4h$$ from the surface of water in a water tank kept on a horizontal surface. If $$\ell << h, r << h$$ and the rate of water flow from the holes is the same, then $$r$$ is equal to

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

Air of density 1.2 kg m$$^{-3}$$ is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are 150 ms$$^{-1}$$ and 100 ms$$^{-1}$$, respectively. The pressure difference between the upper and lower sides of the wings, is :

$$N$$ identical small liquid droplets, each of radius $$r$$, coalesce to form a single large drop of radius $$R$$. If $$\sigma$$ is the surface tension of the liquid, the total energy released in this process is:

Two liquids of densities $$\rho_1$$ and $$\rho_2$$ ($$\rho_2 = 2\rho_1$$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (Assume that the liquids are not mixing):

A tank contains two immiscible liquids of densities $$6\rho$$ and $$2\rho$$. The higher density liquid is filled up to a height $$L/2$$ from the bottom. A thin rod of density $$\rho$$ and length $$L$$ is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium, the time period of small oscillations is $$\dfrac{2\pi}{n}\sqrt{\dfrac{L}{g}}$$, where $$g$$ is the acceleration due to gravity. The value of $$n$$ is:

In a cylindrical water tank, there are two small holes $$A$$ and $$B$$ on the wall at a depth of $$h_1$$, from the surface of water and at a height of $$h_2$$ from the bottom of water tank. Surface of water is at height $$h_2$$ from the bottom of water tank. Surface of water is at height $$H$$ from the bottom of water tank. Water coming out from both holes strikes the ground at the same point $$S$$. Find the ratio of $$h_1$$ and $$h_2$$.

A tube of length L is shown in the figure. The radius of the cross section at point (1) is 2 cm and at point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then the velocity of water leaving point (2) will be

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 the tanks 1 and 2 through the holes, the times taken to empty the tanks are $$t_1$$ and $$t_2$$, respectively. If $$H = \left(\frac{16}{9}\right)h$$, then the ratio $$t_1/t_2$$ is ______.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water colunms in vertical tubes is 5 cm and the area of cross-sections at A and B are $$6cm^{2}$$ and $$3cm^{2}$$ respectively. The rate of flow will be ____ $$cm^{3/s}$$. $$(take g=10m/s^{2})$$

When the chimney is closed using a cap at the top, a pressure difference $$\Delta P$$ develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of $$\Delta P$$ is ____ Nm$$^{-2}$$.

The figure shows a liquid of a given density flowing steadily in a horizontal tube of a varying cross-section. Cross-sectional area at A is $$1.5$$ cm$$^2$$, and that at B is $$25$$ mm$$^2$$, if the speed of liquid at B is $$60$$ cm s$$^{-1}$$ then $$(P_A - P_B)$$ is
(Given $$P_A$$ and $$P_B$$ are liquid pressures at A and B points. Density $$\rho = 1000$$ kg m$$^{-3}$$. A and B are on the axis of tube)

An ideal non-viscous, incompressible fluid flows steadily through a horizontal pipe of varying cross-section. At a point where the cross-sectional area of the pipe is $$A$$, the velocity of the fluid stream is $$v$$ and the static pressure is $$P$$. At another point down the pipe line where the cross-sectional area reduces to $$\frac{A}{3}$$, the static pressure becomes $$\frac{P}{2}$$. If the density of the fluid is $$\rho$$, the initial velocity $$v$$ of the fluid is given by:

A cylindrical block of wood (density = 650 kg m$$^{-3}$$), of base area 30 cm$$^2$$ and height 54 cm, floats in a liquid of density 900 kg m$$^{-3}$$. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly):

A wide tank drains through a small orifice of cross-sectional area $$a$$ located at its side, with the orifice center situated at a depth $$h$$ below the free surface. The tank’s main cross-sectional area $$A$$ is exceptionally large ($$A \gg a$$) and remains essentially constant. Neglecting fluid viscosity and assuming atmospheric pressure acts at both the free upper surface and the exit nozzle, how long does it take for the water level to fall from an initial height $$h_0$$ to a lower height $$h_1$$ ($$h_1 > 0$$)?

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water = 10$$^3$$ kg/m$$^3$$]

An air bubble of radius 1 cm in water has an upward acceleration of 9.8 cms$$^{-2}$$. The density of water is 1 gm cm$$^{-3}$$ and water offers negligible drag force on the bubble. The mass of the bubble is $$(g = 980$$ cm/s$$^2)$$.

A solid sphere, of radius R acquires a terminal velocity $$v_1$$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $$\eta$$. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, $$v_2$$, when falling through the same fluid, the ratio $$\left(\frac{v_1}{v_2}\right)$$ equals:

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 m s$$^{-2}$$)

The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m$$^3$$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:

A horizontal pipe has a non-uniform cross-section. The velocity of water at a point where the radius is $$2r$$ is found to be $$v$$. The velocity of water at another point in the same pipe where the radius is $$r$$ will be:

A small spherical ball of radius $$r$$ falls from rest in a viscous liquid. Due to friction, heat is produced. When the ball attains its terminal velocity, the rate of production of heat is proportional to: