Physics

Fluid Mechanics

673 Questions

Fluid mechanics is a core physics topic that evaluates the principles of liquid pressure, buoyancy, density, and viscosity through complex numerical problems. The questions require calculating the volume of submerged objects, understanding hydraulic jumps, and applying fundamental fluid statics principles. It is a highly scoring subject for candidates preparing for technical and engineering competitive exams.

Liquid pressure and depthBuoyancy and densityVolume expansionHydraulic jump calculationsSurface tension mechanics

Fluid Mechanics Questions

Multiple choice physics superposition of waves-2: stationary (standing) waves: vibrations of air columns determining wavelength and speed of sound resonance tube resonance and sonometer

In a resonance column experiment, the first resonance is obtained when the level of the water in tube is $20 cm$ from the open end. Resonance will also be obtained when the water level is at a distance of

  1. $40 cm$ from the open end.
  2. $60$ cm from the open end.
  3. $80$ cm from the open end.

  4. data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Frequency of first resonance in closed pipe    $\nu = \dfrac{v}{4L _1}$      ....(1)
where $L _1 = 20 \ cm$
Frequency of next resonance in closed pipe  $\nu = \dfrac{3v}{4L _2}$      ....(2)
Equating (1) and (2), we get
$\dfrac{v}{4L _1} = \dfrac{3v}{4L _2}$
$\implies$  $L _2 = 3L _1  = 3\times 20 = 60 \ cm$

Multiple choice viscosity option b: engineering physics properties of matter physics

Viscosity of the fluids is analogous to:

  1. Random motion of the gas molecules

  2. Friction between the solid surfaces

  3. integral motion

  4. Nonuniform motion of solids
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Viscosity is the property by virtue of which a liquid offers resistance for the relative motion between its layer.
Friction is the force between two solid surfaces which offers resistance for the relative motion between them. 
So, viscosity of the fluids is analogous to friction between the solid surfaces.

Multiple choice viscosity option b: engineering physics properties of matter physics

The viscous force on a small sphere of radius $R$ moving in a fluid varies as 

  1. $\propto \ R^2$
  2. $\propto \ R$
  3. $\propto \ (\dfrac{1}{R})$
  4. $\propto \ (\dfrac{1}{R})^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to Stokes' Law, the viscous drag force F on a sphere of radius R moving at velocity v in a fluid is given by F = 6 * pi * eta * R * v. Thus, the force is directly proportional to the radius R.

Multiple choice viscosity option b: engineering physics properties of matter physics

Why does the cotton wick in an oil filled lamp keep on burning?

  1. By friction

  2. By capillary action

  3. By electrostatic force

  4. By Gravitational force
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Due to surface tension of oil capillary rise can be seen in cotton wick which makes lamp to burn.

Multiple choice viscosity option b: engineering physics properties of matter physics

A liquid rises in a capillary tube when the angle of contact is:

  1. $An\ acute\ one$
  2. $An\ obtuse\ one$
  3. $\pi/2\ radian$
  4. $\pi\ radian$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If angle of contact is acute, liquid rises in a capillary tube whereas if angle of contact is obtuse, liquid is depressed in a capillary tube.

Hence, option A is correct.

Multiple choice viscosity option b: engineering physics properties of matter physics

Two solid metal balls of radii $r$ $2r$ are falling with their terminal speeds in a viscous liquid.What is the ratio of drag force acting on these two balls?

  1. 1;2

  2. 1;4

  3. 1;8

  4. 4;1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Terminal velocity v_t is proportional to r^2. The drag force F = 6 * pi * eta * r * v_t. Substituting v_t proportional to r^2, we get F proportional to r * r^2 = r^3. The ratio of forces for radii r and 2r is (r/2r)^3 = 1/8.

Multiple choice viscosity option b: engineering physics properties of matter physics

When $200 ml$ of water is subjected to a pressure of $2 \times {10^8}pa,$ the decrease in its volume is $0.2 ml.$ the compressibility of water is -----

  1. $5 \times {10^{ - 8}}{m^2}{N^{ - 1}}$
  2. $5 \times {10^{ - 10}}{m^2}{N^{ - 1}}$
  3. $5 \times {10^{ - 12}}{m^2}{N^{ - 1}}$
  4. $None$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compressibility K = -(1/V) * (dV/dP). Here, dV/V = 0.2 / 200 = 0.001. dP = 2 * 10^8 Pa. K = 0.001 / (2 * 10^8) = 0.5 * 10^-11 = 5 * 10^-12 m^2/N.

Multiple choice viscosity option b: engineering physics properties of matter physics

An air bubble of diameter 2mm rises steadily througha solution of density $1750 kg/m^3$at the rate of $0.35cm/s$.Calculate the coefficient of viscosity of the solution.The density of air is negligible. 

  1. 10

  2. 11

  3. 12

  4. 13
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The force of buoyancy B is equal to the weight of  the displaced liquid. Thus

$\Rightarrow B=\dfrac{4}{3}\pi r^36g$
This force is upward. The viscous force acting downward is $F=6\pi nrv$
The weight of the air bubble may be neglected as the density of air is small. for uniform velocity -
$\Rightarrow F=B$
$\Rightarrow 6\pi nrv=\dfrac{4}{3}\pi r^3 6g$
$\Rightarrow n=\dfrac{2r^36g}{9v}$
         $=\dfrac{2\times \left( 1\times 106{-3}m\right)^2\times \left( 1750kg/m^3\right)\times 9.8m/s^2}{9\times 0.35\times 10^{-2}m/s}$
         $=11\;poise$
This appears to be a highly viscous liquid.

Multiple choice viscosity option b: engineering physics properties of matter physics

A U-tube having identical limbs is partially filled with water. An immiscible oil having a density of 0.8 g/cc is poured into one side until the water rises by 25 cm on the other side. the level of oil will stand higher than the water level? 

  1. 6.25 cm

  2. 75 cm

  3. 22.5 cm

  4. 12.5 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By hydrostatic equilibrium, the pressure exerted by the oil column must balance the pressure exerted by the displaced water column. Using rho_oil * h_oil = rho_water * h_water with rho_oil = 0.8 g/cc and water rising by 25 cm (meaning the water level difference is 25 cm), we find the oil height is 31.25 cm, making it stand 12.5 cm higher than the final water level.

Multiple choice viscosity option b: engineering physics properties of matter physics

A small sphere of mass M and density $D _1$ is dropped in a vessel filled with glycerine. If the density of glycerine is $D _2$ then the viscous force acting on the ball will be in Newton.

  1. $M D _1 D _2$
  2. $Mg \displaystyle \left [ 1- \frac {D _2}{D _1} \right ]$
  3. $\displaystyle \frac {M D _1 g}{D _2}$
  4. $\displaystyle \frac {M}{g} \left ( D _1 + D _2 \right)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When sphere is in glycerine, three forces acts on it. which balances each other.

  • weight $(W)$
  • buoyant force $(F _B)$
  • viscous force $(F _V)$
and $W=F _B+F _V$
$\Rightarrow Mg=V _g D _2g +F _V$
$\Rightarrow Mg=V _s D _2g +F _V           \because V _g=V _s$
$\Rightarrow Mg=\frac{M}{D _1} D _2g +F _V             \because V _s=\frac{M}{D _1}$
$\Rightarrow F _V=Mg \left [ 1- \frac {D _2}{D _1} \right ]$

Multiple choice viscosity option b: engineering physics properties of matter physics

An air bubble of radius $1 \,cm$ is found to rise in a cylindrical vessel of large radius at a steady rate of $0.2 \,cm$ per second. If the density of the liquid is $1470 \,kg \,m^{-3}$, then coefficient of viscosity of liquid is approximately equal to

  1. $163$ poise
  2. $163$ centi-poise
  3. $140$ poise
  4. $140$ centi-poise
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice viscosity option b: engineering physics properties of matter physics

A capillary tube of area of cross-section A is dipped in water vertically. The amount of heat evolved as the water rises in the capillary tube up to height h is: (The density of water is $\rho$)

  1. $\dfrac{A\rho gh^2}{2}$
  2. $Agh^2\rho$
  3. $2Agh^2\rho$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The potential energy gained by the water column is m * g * h_cm = (A * h * rho) * g * (h/2) = (A * rho * g * h^2) / 2. This energy is provided by the surface tension work, and the heat evolved is the difference between the work done by surface tension and the potential energy gained.

Multiple choice viscosity option b: engineering physics properties of matter physics

An air bubble of radius $1 mm$ moves up with uniform velocity of $0.109ms^{-1}$ in a liquid column of density $14.7 \times 10^{3} kg/m^{3}$, then coefficient of viscosity will be ($g = 10ms^{-2}$)

  1. $1.3 Pa- s$
  2. $300 Pa -s$
  3. $15 Pa- s$
  4. $150 Pa- s$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the bubble is moving up with uniform velocity, the frictional force acting downwards is equal to the buoyant force acting upwards.

$\implies V\rho g=6\pi\eta rv$
$\implies \eta=\dfrac{V\rho g}{6\pi rv}$
$=0.3Pa.s$

Multiple choice viscosity option b: engineering physics properties of matter physics

A solid ball of density half that of water falls freely under gravity from a height of 19.6 m and then enters the water. Up to what depth will the ball go? How much time will it take to come again to the water surface. Neglect air resistance and viscosity effects in water. ($
g=9.8 \mathrm{ms}^{-2}
$)

  1. 4 s

  2. 8 s

  3. 6 s

  4. 2 s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The ball falls 19.6 m, reaching velocity v = sqrt(2gh) = sqrt(2 * 9.8 * 19.6) = 19.6 m/s. In water, the buoyant force exceeds gravity (density is half of water), so it decelerates. The time to stop and return is calculated using the effective acceleration in water.

Multiple choice viscosity option b: engineering physics properties of matter physics

A spherical ball of radius $3\times 10^{-4}\ m$ and density $10^{4}\ kg\ m^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water, the velocity of the ball does not change, then the value of $h$ is (Given, $viscosity >of> water=9.8\times 10^{-6}\ Nsm^{-2}$ and $\rho _{water}=10^{3}\ kgm^{-3}$)

  1. $1650\ m$
  2. $165\ m$
  3. $1050\ m$
  4. $105\ m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the velocity does not change upon entering water, the drag force must balance the net weight in water. F_drag = (m_ball - m_displaced) * g. Using Stokes' Law for F_drag and equating, we solve for the velocity v, then use v^2 = 2gh to find h.