Fluid Mechanics

Two spherical soap bubbles of radii '\(a\)' and '\(b\)' in vacuum coalesce under isothermal conditions. The resulting bubble has a radius equal to

The fundamental frequency of a sonometer wir carrying a block of mass '\(M\)' and density '\(\rho\)' is '\(n\)' Hz. When the block is completely immerse in a liquid of density '\(\sigma\)' then the new frequency will be

Venturimeter is used to

Twenty seven droplets of water each of radius \(0.1 \mathrm{~mm}\) merge to form a single drop then the energy released is

A large number of water droplets each of radius '\(t\)' combine to form a large drop of Radius '\(R\)'. If the surface tension of water is '\(T\)' & mechanical equivalent of heat is '\(\mathrm{J}\)' then the rise in temperature due to this ...

If work done in blowing a soap bubble of volume \(V\) is \(W\), then the work done in blowing the bubble of volume \(2 \mathrm{~V}\) from same soap solution is

There is hole of area \(A\) at the bottom of a cylindrical vessel. Water is filled to a height \(h\) and water flows out in \(t\) second. If water is filled to a height \(4 h\), it will flow out in time (in second)

The excess pressure inside a first spherical drop of water is three times that of second spherical drop of water. Then the ratio of mass of first spherical drop to that of second spherical drop is

A spherical drop of liquid splits into 1000 identical spherical drops. If '\(\mathrm{E}_1\)' is the surface energy of the original drop and '\(\mathrm{E}_2\)' is the total surface energy of the resulting drops, then $$\frac{E_1}{E_2}=\frac{...

Consider a soap film on a rectangular frame of wire of area \(3 \times 3 \mathrm{~cm}^2\). If the area of the soap film is increased to \(5 \times 5 \mathrm{~cm}^2\), the work done in the process will be (surface tension of soap solution is...

Select the WRONG statement from the following. In a streamline flow

A spherical metal ball of radius '\(r\)' falls through viscous liquid with velocity '\(\mathrm{V}\)'. Another metal ball of same material but of radius \(\left(\frac{r}{3}\right)\) falls through same liquid, then its terminal velocity will ...

Eight small drops of mercury each of radius '\(r\)', coalesce to form a large single drop. The ratio of total surface energy before and after the change is

A body of density '\(\rho\)' is dropped from rest at a height '\(h\)' into a lake of density '\(\sigma' (\sigma>\rho)\). The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces)

A spherical liquid drop of radius \(\mathrm{R}\) is divided into 8 equal droplets. If surface tension is \(\mathrm{S}\), then the work done in this process will be

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio \(4: 3\). The rise of liquid in two capillaries is '\(h_1\)' and '\(h_2\)' respectively. If the surface tensions of liqui...

What should be the diameter of a soap bubble, in order that the excess pressure inside it is \(25.6 \mathrm{~Nm}^{-2}\) ? [surface tension of soap solution \(\left.=3 \cdot 2 \times 10^{-2} \mathrm{~Nm}^{-2}\right]\)

A fluid of density '\(\rho\)' is flowing through a uniform tube of diameter '\(d\)'. The coefficient of viscosity of the fluid is '\(\eta\)', then critical velocity of the fluid is

A liquid drop of radius '\(R\)' is broken into '\(n\)' identical small droplets. The work done is [T = surface tension of the liquid]

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid '\(A\)' vertically is \(5 \mathrm{~cm}\). If the tube is dipped in a similar manner in another liquid '\(B\)' of surface tension and density doub...

Three liquids have same surface tension and densities \(\rho_1, \rho_2\), and \(\rho_3\left(\rho_1>\rho_2>\rho_3\right)\). In three identical capillaries rise of liquid is same. The corresponding angles of contact \(\theta_1, \theta_2\) and...

Water flows through a horizontal pipe at a speed '\(\mathrm{V}\)'. Internal diameter of the pipe is '\(\mathrm{d}\)'. If the water is coming out at a speed '\(V_1\)' then the diameter of the nozzle is

A metal sphere of mass '\(m\)' and density '\(\sigma_1\)' falls with terminal velocity through a container containing liquid. The density of liquid is '\(\sigma_2\)'. The viscous force acting on the sphere is

At critical temperature, the surface tension of liquid is

'\(n\)' number of liquid drops each of radius '\(r\)' coalesce to form a single drop of radius '\(R\)'. The energy released in the process is converted into the kinetic energy of the big drop so formed. The speed of the big drop is
$$[\math...

A steel coin of thickness '\(\mathrm{d}\)' and density '\(\rho\)' is floating on water of surface tension '\(T\)'. The radius of the coin \((R)\) is [\(\mathrm{g}=\) acceleration due to gravity]

The work done in blowing a soap bubble of radius \(\mathrm{R}\) is '\(\mathrm{W}_1\)' at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius \(2 \mathrm{R}\) is blown and the work done i...

The excess pressure inside a soap bubble of radius \(2 \mathrm{~cm}\) is 50 dyne/cm\(^2\). The surface tension is

A glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is [radius of tu...

A thin metal disc of radius 'r' floats on water surface and bends the surface downwards along the perimeter making an angle '\(\theta\)' with the vertical edge of the dsic. If the weight of water displaced by the disc is '\(\mathrm{W}\)', ...

The work done in blowing a soap bubble of volume '\(\mathrm{V}\)' is '\(\mathrm{W}\)'. The work required to blow a soap bubble of volume '\(2 \mathrm{~V}\)' is [\(\mathrm{T}=\) surface tension of soap solution]

If the work done in blowing a soap bubble of volume '\(\mathrm{V}\)' is '\(\mathrm{W}\)', then the work done in blowing a soap bubble of volume '\(2 \mathrm{~V}\)' will be

'n' small drops of same size fall through air with constant velocity \(5 \mathrm{~cm} / \mathrm{s}\). They coalesce to form a big drop. The terminal velocity of the big drop is

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. The ratio between their volumes is (Pressure outside the soap bubble is 1 atmosphere)

Water rises to a height of \(2 \mathrm{~cm}\) in a capillary tube. If cross-sectional area of the tube is reduced to \(\frac{1}{16}^{\text {th }}\) of initial area then water will rise to a height of

The speed of a ball of radius \(2 \mathrm{~cm}\) in a viscous liquid is \(20 \mathrm{~cm} / \mathrm{s}\). What will be the speed of a ball of radius \(1 \mathrm{~cm}\) in same liquid?

Work done in increasing the size of a soap bubble from radius of \(3 \mathrm{~cm}\) to \(5 \mathrm{~cm}\) in millijoule is nearly (surface tension of soap solution \(=0.03 \mathrm{~Nm}^{-1}\))

An ice cube of edge \(1 \mathrm{~cm}\) melts in a gravity free container. The approximate surface area of water formed is (water is in the form of spherical drop)

A glass rod of radius '\(r_1\)' is inserted symmetrically into a vertical capillary tube of radius '\(r_2\)' (\(r_1 < \mathrm{r}_2\)) such that their lower ends are at same level. The arrangement is dipped in water. The height to which wate...

Water rises upto a height of \(4 \mathrm{~cm}\) in a capillary tube. The lower end of the capillary tube is at a depth of \(8 \mathrm{~cm}\) below the water level. The mouth pressure required to blow an air bubble at the lower end of the ca...

A drop of liquid of density '\(\rho\)' is floating half immersed in a liquid of density '\(d\)'. If '\(T\)' is the surface tension, then the diameter of the drop of the liquid is

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

A needle is \(7 \mathrm{~cm}\) long. Assuming that the needle is not wetted by water, what is the weight of the needle, so that it floats on water?
\(\left[\mathrm{T}=\right.\) surface tension of water $$\left.=70 \frac{\mathrm{dyne}}{\math...

A ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of the material of the ball. The viscous force of the liquid on the rising ball is greater than the weight of the ball by a ...

If the terminal speed of a sphere A [density \(\rho_{\mathrm{A}}=7.5 \mathrm{~kg} \mathrm{~m}^{-3}\) ] is \(0.4 \mathrm{~ms}^{-1}\), in a viscous liquid [density \(\rho_{\mathrm{L}}=1.5 \mathrm{~kg} \mathrm{~m}^{-3}\) ], the terminal speed ...

Two small drops of mercury each of radius '\(R\)' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

The velocity of a small ball of mass '\(M\)' and density '\(\mathrm{d}_1\)' when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is '\(\mathrm{d}_2\)', the viscous force acting on t...

The surface tension of most of the liquid decreases with rise in

A big water drop is divided into 8 equal droplets. \(\Delta \mathrm{P}_{\mathrm{s}}\) and \(\Delta \mathrm{P}_{\mathrm{B}}\) be the excess pressure inside a smaller and bigger drop respectively. The relation between $$\Delta \mathrm{P}_{\ma...

Water rises upto a height \(10 \mathrm{~cm}\) in a capillary tube. It will rise to a height which is much more than \(10 \mathrm{~cm}\) in a very long capillary tube if the apparatus is kept.