Fluid Mechanics

A spherical liquid drop splits in to 729 identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of resulting drops, then $\frac{E}{U}=\frac{1}{x}$. The value of $x$ is

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

A capillary tube when immersed vertically in water, the rise of water column is upto height $h_1$ on earth's surface. When this arrangement is taken into a mine of depth 'd', below earth's surface, the height of the water column is $\mathrm...

125 small water drops of same size fall through air with constant velocity $4 \mathrm{~cm} / \mathrm{s}$. They coalesce to form a big drop. The terminal velocity of the big drop is

The work done in splitting a water drop of radius R into 64 droplets is ( $\mathrm{T}=$ surface tension of water)

Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ coalesce to form a big drop. The radius of the big drop is

When one end of the capillary is dipped in water, the height of water column is ' $h$ '. The upward force of 108 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillar...

The velocity of small spherical ball of mass ' $m$ ' and density ' $\mathrm{d}_1$ ', when dropped in a container filled with glycerine becomes constant after some time. The viscous force acting on the ball if density of glycerine is ' $\mat...

In a capillary tube of area of cross-section 'a' water rises to height ' $h$ '. To what height will water rise in a capillary tube of area of cross-section $4 a$ ?

The amount of work done in blowing a soap bubble such that its diameter increases from 'd' to ' $D$ ' is ( $T=$ surface tension of solution)

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^2$, the velocity of water is $1 \mathrm{~m} / \mathrm{s}$ and pressure is 2000 Pa . The pressure of wate...

When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capil...

The excess pressure inside first soap bubble is three times that of a second soap bubble. The ratio of volumes of the first to second bubble

A wind with speed $50 \mathrm{~m} / \mathrm{s}$ blows parallel to the roof of a house. The area of the roof is $300 \mathrm{~m}^2$. Assume that the pressure inside the house is atmospheric pressure. Density of air is $1.2 \mathrm{~kg} / \ma...

A disc of paper of radius ' $R$ ' has a hole of radius ' $r$ '. It is floating on a liquid of surface tension ' T '. The force of surface tension on the disc is

A solid cylinder of length $l$ and cross-sectional area $\frac{a}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $l / 4$ in the denser liquid as shown in figure. The lower density liqui...

The energy needed for breaking a liquid drop of radius ' $R$ ' into 216 droplets, each of radius ' $r$ ' is ' $x$ ' times $T R^2$. The value of ' $x$ ' is [ $T=$ surface tension of the liquid].

The amount of work done in blowing a soap bubble such that its diameter increases from $\mathrm{d}_1$ to $\mathrm{d}_2$ is ( $\mathrm{T}=$ surface tension of soap solution)

There are two identical small holes on the opposite side of a tank containing full of a liquid. The tank is open at the top. The difference in height between the two holes is ' $h$ '. As the liquid comes out of the two holes, the tank will ...

A capillary tube is taken from earth's surface to moon's surface. The rise of liquid column on the moon's surface is (acceleration due to gravity on the earth's surface is six times that of moon's surface)

A rectangular film of liquid is expanded from $(5 \mathrm{~cm} \times 4 \mathrm{~cm})$ to $(7 \mathrm{~cm} \times 8 \mathrm{~cm})$. If the work done is $3 \times 10^{-4} \mathrm{~J}$, the surface tension of the liquid is (nearly)

Water rises in a capillary tube of radius r upto ${ }^2$ height h . The mass of water in a capillary is m. The mass of water that will rise in capillary of radius $\frac{\mathrm{r}}{5}$ will be

The excess pressure inside a soap bubble is 1.5 times the excess pressure inside a second soap bubble. The volume of the second bubble is ' $x$ ' times the volume of the first bubble. The value of ' x ' is

The energy needed for breaking a liquid drop of radius ' $R$ ' into ' $n$ ' droplets each of radius ' $r$ ' is $[\mathrm{T}=$ surface tension of the liquid]

An incompressible fluid flows steadily through a cylindrical pipe having radius R at point A and $\left(\frac{\mathrm{R}}{3}\right)$ at point B further along the direction of flow of liquid. If the velocity at point A is ' V ' then that at ...

A liquid drop of volume V is placed on the surface of glass plate. Then another glass plate is placed on it such that liquid forms a thin layer of area A between the surfaces of two plates. To separate the plates a force F has to be applied...

Water flows through a horizontal pipe of varying cross-section at the rate of $\pi \times 10^{-1} \mathrm{~m} / \mathrm{s}$. The velocity of water at a point where the radius of the pipe is 10 cm is $(\pi=3.14)$

Two capillary tubes of same diameter are kept vertically in two liquids whose densities are in the ratio $4: 3$. If their surface tensions are in the ratio $6: 5$, the ratio of heights $\left(\frac{h_1}{h_2}\right)$ of liquids in the two ca...

In air, a charged soap bubble of radius R breaks into 64 small soap bubbles of equal radius $r$. The ratio of mechanical force per unit area of big soap bubble to that of a small bubble is

A liquid drop having surface energy $E$ is spread into 729 droplets of same size. The final surface energy of the droplets is

A water drop of $0.01 \mathrm{~cm}^3$ is squeezed between two glass plates and spreads in to area of $10 \mathrm{~cm}^2$. If surface tension of water is 70 dyne $/ \mathrm{cm}$ then the normal force required to separate glass plates from ea...

The surface energy of a liquid drop is ' $V$ '. It is sprayed into 1000 equal droplets. The surface energy of all the droplets is

A liquid drop having surface energy $E$ is sprayed into 512 droplets of same size. The final surface energy is

Two raindrops reach the earth with different terminal velocities having the ratio $9: 4$. The ratio of their volumes is

Pure water rises through a height $h$ in a capillary tube of internal radius r . Surface tension of water is T . The pressure difference between the water level in the container and the lowest point of the concave meniscus is

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but diameter is doubled. If pressure on the surface is $h$ meter of mercury column and relative density of mercury is ' $\rho$ ' then the depth ...

When a big drop of water is formed from ' $n$ ' small drops of water, the energy loss is ' 3 E ' where ' $E$ ' is the energy of the bigger drop. The radius of the bigger drop is ' R ' and that of smaller drop is ' $r$ ' then the value of ' ...

One end of a capillary tube is dipped in water, the rise of water column is ' $h$ '. The upward force of 98 dyne due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary...

A liquid rises to a height of 2.4 cm in a glass capillary P. Another glass capillary Q having diameter $80 \%$ of capillary $P$ is immersed in the same liquid. The rise of liquid in capillary $Q$ is

' $n$ ' small water drops of same size (radius $r$ ) fall through air with constant velocity V. They coalesce to form a big drop of radius R . The terminal velocity of the big drop is

Water is flowing steadily in a river. A and B are the two layers of water at heights 40 cm and 90 cm from the bottom. The velocity of the layer A is $12 \mathrm{~cm} / \mathrm{s}$. The velocity of the layer B is

A small metal sphere of density $\rho$ is dropped from height $h$ into a jar containing liquid of density $\sigma(\sigma>\rho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces)

Water is flowing in a conical tube as shown in figure. Velocity of water at area ' $\mathrm{A}_2$ ' is $60 \mathrm{~cm} / \mathrm{s}$. The value of ' $\mathrm{A}_1$ ' and ' $\mathrm{A}_2$ ' is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ resp...

When an air bubble rises from the bottom of lake to the surface, its radius is doubled. The atmospheric pressure is equal to that of a column of water of height ' $H$ '. The depth of the lake is

Let ' $n$ ' is the number of liquid drops, each with surface energy ' $E$ '. These drops join to form single drop. In this process

Three liquids of densities $\rho_1, \rho_2$ and $\rho_3$ (with $\rho_1>\rho_2>\rho_3$ ) having same value of surface tension T , rise to the same height in three identical capillaries. Angle of contact $\theta_1, \theta_2$ and $\theta_3$ re...

The work done in splitting a water drop of radius R into 64 droplets is ( $\mathrm{T}=$ Surface tension of water)

Two identical drops of water are falling through air with steady velocity ' V '. If the two drops come together to form a single drop. The new velocity of the single drop is

The surface of water in a water tank of cross section area $750 \mathrm{~cm}^2$ on the top of a house is ' $h$ ' $m$ above the tap level. The speed of water coming out through the tap of cross section area $500 \mathrm{~mm}^2$ is $30 \mathr...

The excess pressure inside a spherical drop of water A is four times that of another drop B. Then the ratio of mass of drop $A$ to that of drop $B$ is