Physics

Fluid Mechanics

637 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 option b: engineering physics buoyancy floatation fluid pressure

What should be the height of liquid in a cylindrical vessel of diameter d so that the total force on the vertical surface of the vessel be equal to the force on the bottom,

  1. $d$
  2. $2d$
  3. $4d$
  4. $\dfrac{d}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is identical to the previous question. The force on the bottom is rho * g * h * Area, and the force on the side is the integral of pressure over the depth, resulting in h = d/2.

Multiple choice physics option b: engineering physics buoyancy floatation fluid pressure

To what height should a cylindrical vessel be filled with a homogeneous liquid to make the force with which the liquid pressure on the sides of the vessel equal to the force exerted by the liquid on the bottom of the vessel?

  1. Equal to the radius.

  2. Less than radius

  3. More than radius

  4. Four times of radius
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
If  $h$ is the height of liquid in cylinder, $r $ be the radius of the cylinder and $ ρ$ be the density of the liquid.

Then we have
Weight of the liquid $=\pi r^2h \rho g$........................................(I)
Mean pressure on the wall $=\dfrac12 \rho  gh$

The total force on the wall =  $ 2\pi rh \times \dfrac12 \rho  gh= \pi rh^2\rho g $....................................(2)

On equating (I) and (2) we have
$\pi r^2h \rho g=\pi rh^2\rho g $
$r=h$
$\therefore$ The liquid should be filled up-to a height equal to the radius of the cylinder.
Multiple choice physics option b: engineering physics buoyancy floatation fluid pressure

A small hollow vessel open to atmosphere having a small circular hole radius $R\ mm$  in its base is immersed in a tank of water. To what depth should the base of vessel be immersed in water so that water will start coming into the vessel through the hole. ($TT$ is surface tension of water) ($\rho=$density of water).

  1. $\dfrac {2T}{\rho g R}$
  2. $\dfrac {T}{\rho g R}$
  3. $\dfrac {T}{4\rho g R}$
  4. $\dfrac {4T}{\rho g R}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Water enters the vessel when the pressure due to depth (rho * g * h) exceeds the capillary pressure (2T / R) at the hole. Thus, h = 2T / (rho * g * R).

Multiple choice physics option b: engineering physics buoyancy floatation fluid pressure

A tank with a square base of area 2 m$^2$ is divided into two compartments by a vertical partition in the middle. There is a small hinged door of face area 20 cm$^2$ at the bottom of the partition. Water is filled in one compartment and an acid of relative density 1.53 x 10 kg m$^{-3}$ in the other, both to a height of 4 m. The force necessary to keep the door closed is (Take g = 10 m s$^{-2}$)

  1. 10 N

  2. 20 N

  3. 40 N

  4. 80 N
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The situation is as shown in the figure.
For compartment contain water,
$h = 4 m, \rho _w = 10^3\, kg \,m^{-3}$
Pressure exerted by the water at the door at the bottom is
$P _w=\rho _w hg  $

$=10^3\,kg \,m^{-3} \times 4 \,m \times 10 \,m s^{-2}$
$= 4 \times 10^4\,N\,m^{-2}$
For compartment containing acid.
$\rho _a =1.5 \times 10^3\, kg\, m^{-3}, h = 4 \,m$
Pressure exerted by the acid at the door at the bottom is
$P _a=\rho _ahg $
$= 1.5 \times 10^3\,kg \,m^{-3} \times 4\,m \times 10\,m\,s^{-2} $
$= 6 \times 10^4\,N\,m^{-2}$
$\therefore$ Net pressure on the door =$P _a - P _w = (6  \times 10^4 - 4 \times 10^4) N \,m^{-2}$

$= 2 \times 10^4 \,N \,m^{-2}$
Area of the door $= 20 cm^2 = 20 \times 10^{-4} m^2$
$\therefore$ Force on the door$= 2 \times 10^4 N m^{-2} \times 20 \times 10^{-4} m^2 = 40 N$
Thus, to keep the door dosed the force of $40 N$ must be applied horizontally from the water side.

Multiple choice physics option b: engineering physics buoyancy floatation fluid pressure

A vessel, whose bottom has round holes with diameter 0.1 mm, is filled with water. The maximum height up to which water can be filled without leakage is:

  1. 100 cm

  2. 75 cm

  3. 50 cm

  4. 30 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sln :
For equilibrium,
Total upward force by surface tension 
= Weight of the water in tube
$\Rightarrow \, \pi \, \times \, D \, \times$ surface tension (circumference)
$= \, \pi(D/2)^2 \, \times \, h \, \times \, density \, \times \, g(cross \, section)$
where D (diameter) = 0.1 mm = 0.01 cm
Density of water = 1 $\times \, 10^{-3} \, gcm^3$
$\Rightarrow \, \pi \, \times \, (0.01) \, \times \, 75 \, \times \, 10^{-3}$
$= \, \pi \times \, \left(\dfrac{0.01}{2} \right)^2 \, \times \, h \, \times \, 1 \, \times \, 10^{-3} \, \times \, 1000$
$\therefore \, h = \, \dfrac{0.75 \, \times \, 0.01 \, \times \, 4}{0.01 \, \times \, 0.01}$ = 0.3 m = 30 cm

Multiple choice zoology meaning of life energy flow and loss energy flow in a food chain energy flows
Read the passage and answer the following question.

Assume you had a 10m$^2$ pond to study. You measured the amount of light energy bathing the water surface at 1,000kcal.


Based on the energy captured, about what percentage of that would be transferred to higher trophic levels?

  1. 1.65 percent

  2. 16.5 percent

  3. 33 percent

  4. 3.3 percent

  5. 66 percent
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ecological efficiency, or the percentage of energy transferred between trophic levels, is typically around 10 percent to 20 percent. 16.5 percent is a plausible value within this range.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A cube of size 10 cm is floating in equilibrium in a tank of water. When a mass of 10 gm is placed on the cube, the depth of cube inside water increases by $\mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 }$ density of water $= 1000 \mathrm { kg } / \mathrm { m } ^ { 3 } )$

  1. 0.1 m

  2. 1 mm

  3. 1 m

  4. 0.31 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let $x$ be the initial depth upto which the cube is sinked in water.

Let $d$ be the density of the cube
Then
$x\times 10 \times 10\times 1 \times g$
$=10\times 10 \times 10\times 1 \times g\times d$........(1) 
$\Rightarrow x=10d$
Let $x^1$ be the new depth, then 
$x^1\times 100 \times g=1000\times d \times g+10g$........(2)
subtracting (1) and (2) we get
$\Rightarrow 100x^1=10x+10$
$x^2-x= \frac{1}{10cm}=1mm$
Hence,
option $B$ is correct answer.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

Statement I:- A block is immersed in a liquid inside a beaker,which is falling freely. Buoyant force acting on block is zero.
Statement II:- In case of freely falling liquid there is no pressure difference between any two points.

  1. Statement I is true,statement II is true and statement II is a correct explanation for statement I.

  2. Statement I is true,Statement II is true and statement II is NOT the correct explanation for statement I.

  3. Statement I is true,Statement II is false.

  4. Statement I is false,Statement II is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a freely falling frame, the effective gravity is zero. Since buoyant force depends on the pressure gradient caused by gravity, the pressure gradient vanishes, making the buoyant force zero.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

Ice floats on the surface of water because its density is ______ that of water.

  1. more than

  2. less than

  3. same as

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

TRUE
Ice floats in water because it is less dense than water. So any substance that has a lower density in its solid state than in its liquid state will float.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A block of wood floats in water with two-third of its volume submerged. Find the density of wood. Density of water is $10^3\ kg/m^3.$

  1. 0.67

  2. 0.76

  3. 0.82

  4. 0.28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a floating object, the weight of the object equals the weight of the displaced fluid. Thus, density_wood * V_total = density_water * V_submerged. Given V_submerged = (2/3)V_total, the density of wood is (2/3) * 1000 kg/m^3 = 666.7 kg/m^3, which is 0.667 g/cm^3.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

A body of density $\rho$ sinks in a liquid of denisty $\rho _L$. The densities $\rho$ and $\rho _L$ are related as:

  1. $\rho = \rho _L$
  2. $\rho < \rho _L$
  3. $\rho > \rho _L$

  4. nothing can be said
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to archimedes principle a body floats in a fluid if the density of the body is less than that of the fluid.
If the density of body is greater than that of fluid, it will sink.
In the above case, Since the body has  a higher density, therefore it will sink.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

State whether true or false:

Ice is less dense than water (because it has more volume for the same mass), which is why ice floats on water.

  1. True

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

Answer is A.

As water is cooled down, however, the molecules have less energy and hydrogen bonding takes over. The molecules form a ordered crystal through hydrogen bonding that spaces the molecules farther apart than when they were in a liquid. This makes ice less dense than water allowing it to float.
Hence, the statement is true.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

What can you say about the average density of a ship floating on water in relation to the density of water?

  1. Average density of ship is more than the density of water.

  2. Average density of ship is less than the density of water.

  3. Average density of ship is equal to the density of water.

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average density of ship is less than the density of water.

It is important to realize that, while they are related to it, the principle of flotation and the concept that a submerged object displaces a volume of fluid equal to its own volume are not Archimedes' principle. Archimedes' principle, as stated above, equates the buoyant force to the weight of the fluid displaced.
So, according to law of flotation, a body will float in a fluid if it has less density than the fluid.
So, in order for the ship to float, its average density must be less than the water.

Multiple choice physics upthrust in fluids, archimedes' principle and floatation applications of floatation principle of floatation and its applications when do objects float on water?

Give reasons as to why bodies like cork or wood float in water.

  1. They are denser than water

  2. They are less dense than water

  3. They have the same density as that of water

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

Density of cork or wood are less than that of water hence they float in water