Fluid Mechanics

A wooden block of outer volume 1 litre and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then, the volume of the cavity is

The maximum length of water column that can stay without falling in a vertically held capillary tube of diameter 1 mm and open at both the ends is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ and surface tension of water $=0.07 \mat...

A cube of side 40 cm is floating with $\frac{1}{4}$ th of its volume immersed in water. When a circular disc is placed on the cube, it floats with $\frac{2}{5}$ th of its volume immersed in water. The mass of the disc is

If $W_1$ is the work done in increasing the radius of a soap bubble from ' $r$ ' to ' $2 r$ ' and $W_2$ is the work done in increasing the radius of the soap bubble from ' $2 r$ ' to ' $3 r$ ', then $W_1: W_2=$

An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is $125 \%$ more than its surface area at the bottom of the tank. If the ...

A thin film of water is formed between two straight parallel wires each of length 8 cm separated by distance of 0.6 cm . The work done to increase the distance between the wires to 0.8 cm is (Surface tension of water $=0.07 \mathrm{Nm}^{-1}...

A rain drop of diameter 1 mm falls with a terminal velocity of $0.7 \mathrm{~ms}^{-1}$ in air. If the coefficient of viscosity of air is $2 \times 10^{-5} \mathrm{~Pa}$-s, the viscous force on the rain drop is

Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of $18 \mathrm{~ms}^{-1}$, then the time taken by the body to reach the ground is nearly

If the terminal velocity of a metal sphere of mass 8 g falling through a liquid is $3 \mathrm{cms}^{-1}$, then the terminal velocity of another sphere of mass 64 g made of the same metal falling through same liquid is

The work done in blowing a soap bubble of diameter 3 cm is (surface tension of soap solution $=0.035 \mathrm{Nm}^{-1}$ )

Water is filled in a tank up to a height of 20 cm from the bottom of the tank. Water flows through a hole of area $1 \mathrm{~mm}^2$ at its bottom. The mass of the water coming out from the hole in a time of 0.6 s is

For which of the following Reynold's number, a flow is streamlined?

The height of water level in a tank of uniform cross-section is 5 m . The volume of the water leaked in 5 s through a hole of area $2.4 \mathrm{~mm}^2$ miade at the bottom of the tank is (Assume the level of the water in the tank remains co...

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 mm . If the density of the oil is $900 \mathrm{~kg} \mathrm{~m}^{-3}$, then the surface tension of the soap solution is (...

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point, where the diameter of the pipe becomes 2 cm is

If the excess pressures inside two soap bubbles are in the ratio $2: 3$, then the ratio of the volumes of the somp bubbles is

The velocities of air above and below the surfaces of a flying aeroplane wing are $50 \mathrm{~ms}^{-1}$ and $40 \mathrm{~ms}^{-1}$, respectively. If the area of the wing is $10 \mathrm{~m}^{2}$ and the mass of the aeroplane is 500 kg , the...

A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is $0.9 \mathrm{~g} \mathrm{~cm}^{-3}$, the mass of the wooden cube is

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_{A} \rho_{B}$ and $\rho_{C}$, respectively. If $\rho_{A} > \rho_{B} > \rho_{C}$, then the pressure at the bottom of the ...

A cylindrical vessel, open at the top, contains 15 litres of water. Water drains out through a small opening at the bottom. 5 litre of water comes out in time $t_1$, the next 5 litre in further time $t_2$, and the last 5 litre in further ti...

A cylinder of mass $m$ and material density $\rho$ hanging from a string is lowered into a vessel of cross-sectional area $A$ containing a liquid of density $\sigma(<\rho)$ until it is fully immersed. The increase in pressure at the bottom ...

A water drop breaks into 64 identical droplets of each surface area $10^{-7} \mathrm{~m}^2$. If the surface tension of water is $0.07 \mathrm{Nm}^{-1}$, the increase in the surface energy in the process is

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $H$ is the atmospheric pressure expressed in terms of water column height, then the depth ...

A liquid is taken in a long vertical cylindrical vessel and the cylinder is rotated about its vertical axis as shown in figure. During rotation, the liquid rises along its sides. If the radius of vessel is 0.05 m and speed of rotation is $1...

A vessel having small hole in the bottom has to hold water without leakage, if water is poured into if upto a height of 7 cm . Then the radius of the hole is (surface tension of water is $0.07 \mathrm{Nm}^{-1}$, angle of contact is $0^{\cir...

In a well the pressure at a point 10 m below the surface of water is $\left(g=10 \mathrm{~ms}^{-2}\right)$

The angle of contact is $120^{\circ}$ when a cylindrical rod is vertically placed in a liquid. If the same rod is placed horizontally in the liquid, then the angle of contact is

A straw of circular cross-section of radius $R$ and negligible thickness is dipped vertically into a liquid of surface tension $T$. If the contact angle between the liquid and the straw material is $53^{\circ}$. The force acting on the stra...

A solid metal sphere released in a vertical liquid column has attained terminal velocity in the downward direction. The magnitudes of viscous force, buoyant force and gravitational force acting on it are $F_V, F_B$ and $F_W$ respectively. T...

If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing the soap bubble of radius $2 R$ is

Three identical vessels are filled with three liquids ${ }_{A, B}$ and $C$ with equal masses but having densities $\rho_{A, \rho_B}$ and $\rho_C$ respectively. If $\rho_A>\rho_B>\rho_C$ then the pressure at the bottom of the vessels will be

A soap bubble of initial radius $R$ is to be blown up. The surface tension of the soap film is $T$. The surface energy needed to double the diameter of the bubble is

A venturimeter has a pipe diameter of 4 cm and a throat diameter of 2 cm . Velocity of water in the pipe section is $10 \mathrm{~m} / \mathrm{s}$. The pressure drop, between pipe section and the throat section is (use, density of water $=10...

A spherical drop of radius $r$ is divided into 8 equal droplets. If the surface tension is $S$, then the work done in the process will be

A wide cylindrical vessel 50 cm in height is filled with water and rests on a table. Assuming the viscosity to be negligible. Find at what height from the bottom of the vessel a small hole should be made for the water jet coming out of it t...

A liquid flows steadily through a cylindrical pipe having a radius $2 R$ at a point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity at point $B$ is $4 v$, what will be the velocity at point $A$ ?

In the figure, the chamber $A$ contains a gas, movable chamber $B$ is placed on the top of the gas and it contains $n$ metal balls. The weight of chamber $B$ is supported by the gas. Chamber $C$ has vacuum. Let the gas be in equilibrium at ...

Consider an increase of $1 \%$ in each of radius of artery, viscosity of blood and density of blood, respectively. The percentage change in flow rate of blood in artery is

A metal cube of side 10 cm rests on a film of a liquid of thickness 0.2 mm . If upon applying a horizontal force $\mathbf{F}$ of magnitude 0.1 N . The cube slides with a constant speed of $0.08 \mathrm{~m} / \mathrm{s}$, then the coefficien...

An air bubble of radius 1 mm is at a depth of 8 cm below the free surface of a liquid column. If the surface tension and density of the liquid is $0.1 \mathrm{~N} / \mathrm{m}$ and 2000 $\mathrm{kg} / \mathrm{m}^3$, respectively, by what am...

A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$, the...

A hollow spherical body of outer and inner radii of 4 cm and 2 cm respectively, floats half submerged in a liquid of density $2.0 \mathrm{~g} / \mathrm{cm}^3$. The density of the material of the sphere is

What is the terminal velocity of a rain drop of radius 0.02 mm ?
[Note that the coefficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{N} / \mathrm{m}^2$, density of water is $1000 \mathrm{~kg} / \mathrm{m}^3$. Use, $g=10 \mathrm{~m...

A hydraulic lift as shown in the figure is used to lift a mass of 1000 kg , which is placed on a piston $\left(P_1\right)$ of area $1 \mathrm{~m}^2$. If the cross-section area of the piston $\left(P_2\right)$ at the other end is $0.01 \math...

A block of iron contains a hollow cavity as shown below. The block weighs 6000 N in air and 4000 N in water. If the density of iron and water are $6 \mathrm{~g} / \mathrm{cm}^3$ and $1 \mathrm{~g} / \mathrm{cm}^3$, then the volume of the ca...

The change in surface energy when a big spherical drop fo radius $R$ is split into $n$ spherical droplets of radius $r$ is ( $T=$ surface tension)

A meniscus drop of radius 1 cm is sprayed into $10^6$ droplets of equal size. Calculate the energy expended if surface tension of mercury is $435 \times 10^{-3} \mathrm{~N} / \mathrm{m}$.

A cubical block of wood having mass of 160 g has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. Specific gravity of wood is 0.8 and that metal...