Fluid Mechanics

Water rises up to height ' $X$ ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' d ' in a mine, the water level rises up to height ' $Y$ '. If ' $R$ ' is the radius of earth then the ratio ...

Identify the correct figure which shows the relation between the height of water column in a capillary tube and the capillary radius.

A hemispherical portion of radius ' $R$ ' is removed from the bottom of a cylinder of radius ' R '. The volume of the remaining cylinder is ' V ' and its mass is ' M '. It is suspended by a string in a liquid of density ' $\rho$ ', where it...

A water film is formed between two parallel wires of 10 cm length. The distance of 0.5 cm between the wires is increased by 1 mm . The work done in the process is (surface tension of water $=72 \mathrm{~N} / \mathrm{m}$)

A metal ball of radius $9 \times 10^{-4} \mathrm{~m}$ and density $10^4 \mathrm{~kg} / \mathrm{m}^3$ falls freely under gravity through a distance ' h ' and enters a tank of water. Considering that the metal ball has constant velocity, the ...

The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their respective radii (A to B) is (outside pressure $=1 \mathrm{~atm}$.)

A gardening pipe having an internal radius ' $R$ ' is connected to a water sprinkler having ' $n$ ' holes each of radius ' $r$ '. The water in the pipe has a speed ' $v$ '. The speed of water leaving the sprinkler is

A liquid drop of density ' $\rho$ ' is floating half immersed in a liquid of density ' $d$ '. If ' $T$ ' is the surface tension then the diameter of the liquid drop is ( $\mathrm{g}=$ acceleration due to gravity)

The pressure inside a soap bubble $A$ is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of volume of bubble A to that of B is [Surrounding pressure $=1$ atmosphere]

A steel ball of radius 6 mm has a terminal speed of $12 \mathrm{cms}^{-1}$ in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?

A streamline flow of a liquid of density ' $\rho$ ' is passing through a horizontal pipe of crosssectional area $A_1$ and $A_2$ at two ends. If the pressure of liquid is ' P ' at a point where flow speed is ' $v$ ', then pressure at another...

The pressure inside a soap bubble A is 1.01 atmosphere and that in a soap bubble B is 1.02 atmosphere. The ratio of volume of $A$ to that of $B$ is

Glycerine of density $1.25 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ is flowing in conical shaped horizontal pipe. Crosssectional area of the pipe at its both ends is $10 \mathrm{~cm}^2$ and $5 \mathrm{~cm}^2$ respectively. Pressure differen...

A drum of radius ' $R$ ' full of liquid of density ' $d$ ' is rotated at angular velocity ' $\omega$ ' $\mathrm{rad} / \mathrm{s}$. The increase in pressure at the centre of the drum will be

A ball rises to surface at a constant velocity in liquid whose density is 4 times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is

Liquid drops are falling slowly one by one from vertical glass tube. The relation between the weight of a drop ' $w$ ', the surface tension ' $T$ ' and the radius ' $r$ ' of the bore of the tube is (Angle of contact is zero)

A cylinder contains water upto a height ' $H$ '. It has three orifices $\mathrm{O}_1, \mathrm{O}_2, \mathrm{O}_3$ as shown in the figure. Let $V_1, V_2, V_3$ be the speed of efflux of water from the three orifices. Then

When capillary is dipped vertically in water, rise of water in capillary is ' h '. The angle of contact is zero. Now the tube is depressed so that its length above the water surface is $\frac{\mathrm{h}}{3}$. The new apparent angle of conta...

In most liquids, with rise in temperature, surface tension of a liquid

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

A water drop is divided into 8 equal droplets. The pressure difference between the inner and outer side of the big drop will be

On the surface of the liquid in equilibrium, molecules of the liquid possess

When a mercury drop of radius ' $R$ ' splits up into 1000 droplets of radius ' $r$ ', the change in surface energy is ( $T=$ surface tension of mercury)

The angle of contact between glass and water is $0^{\circ}$ and water rises in a glass capillary upto 6 cm (Surface tension of water is T). Another liquid of surface tension ' $2 \mathrm{~T}^{\prime}$ ', angle of contact $60^{\circ}$ and re...

Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio $4: 3$. If the surface tensions of these two liquids are in the ratio $6: 5$, then the ratio of rise of ...

The viscous force between two liquid layers is

A ball rises to surface at a constant velocity in liquid whose density is 3 times greater than that of the material of the ball. The ratio of force of friction acting on the rising ball to its weight is

The work done in blowing a soap bubble of radius $R$ is $W_1$ at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius 2 R is blown and the work done is $\mathrm{W}_2$. Then

A big water drop is formed by the combination of ' $n$ ' small water droplets of equal radii. The ratio of the surface energy of ' $n$ ' droplets to the surface energy of the big drop is

Water rises in a capillary tube of radius ' $r$ ' up to height ' $h$ '. The mass of water in capillary is ' $m$ '. The mass of water that will rise in capillary of radius $\mathrm{r} / 3$ will be

A capillary tube stands with its lower end dipped into liquid for which the angle of contact is $90^{\circ}$. The liquid will

A lead sphere of mass ' $m$ ' falls in viscous liquid with terminal velocity $\mathrm{V}_0$. Another lead sphere of mass ' 8 m ' but of same material will fall through the same liquid with terminal velocity

Two rain drops of same radius are falling through air each with a steady speed of $5 \mathrm{~cm} / \mathrm{s}$. If the drops coalesce, the new steady velocity of big drop will be

A completely filled water tank of height ' $h$ ' has a hole at the bottom. The total pressure of the bottom is 4 H and atmospheric pressure is H . The velocity of water flowing out of the hole is ( $\rho=$ density of water)

A metal sphere of radius R, density $\rho_1$ moves with terminal velocity $\mathrm{V}_1$ through a liquid of density $\sigma$. Another sphere of same radius but density $\rho_2$ moves through same liquid. Its terminal velocity is $\mathrm{V...

A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $\mathrm{P}_2$. The speed of water flowing out of the pipe is ($\rho=$ density of water)

A glass capillary of radius 0.35 mm is inclined at $60^{\circ}$ with the vertical in water. The height of the water column in the capillary is (surface tension of water $=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}$, acceleration due to gravi...

Two metal spheres are falling through a liquid of density $2.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ with the same uniform speed. The density of material of first sphere and second sphere is $11.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$...

Two soap bubbles having radii ' $r_1$ ' and ' $r_2$ ' has inside pressure ' $P_1$ ' and ' $\mathrm{P}_2$ ' respectively. If $\mathrm{P}_0$ is external pressure then ratio of their volume is

The radii of two soap bubbles are \(r_1\) and \(r_2\). In isothermal condition they combine with each other to form a single bubble. The radius of resultant bubble is

The excess of pressure in a first soap bubble is three times that of other soap bubble. Then the ratio of the volume of first bubble to other is

Water is flowing through a horizontal pipe in stream line flow. At the narrowest part of the pipe

A fluid of density '\(\rho\)' and viscosity '\(\eta\)' is flowing through a pipe of diameter '\(d\)', with a velocity '\(v\)'. Reynold number is

A soap bubble of radius '\(R\)' is blown. After heating a solution, a second bubble of radius '\(2 \mathrm{R}\)' is blown. The work required to blow the \(2^{\text {nd }}\) bubble in comparison to that required for the \(1^{\text {st }}\) b...

A film of soap solution is formed between two straight parallel wires of length \(10 \mathrm{~cm}\) each separated by \(0.5 \mathrm{~cm}\). If their separation is increased by \(1 \mathrm{~mm}\) while still maintaining their parallelism. Ho...

Water rises in a capillary tube of radius '\(r\)' upto a height '\(h\)'. The mass of water in a capillary is '\(m\)'. The mass of water that will rise in a capillary tube of radius \(\frac{'r'}{3}\) will be

The potential energy of a molecule on the surface of a liquid compared to the molecules inside the liquid is

By adding soluble impurity in a liquid, angle of contact

It is easier to spray water to which soap is added because addition of soap to water

1000 small water drops of equal size combine to form a big drop. The ratio of final surface energy to the total initial surface energy is