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 maths application of derivatives - iii second derivative test maxima and minima application of derivatives

According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at $t$ hours past $2:00$ in the morning is given by $\displaystyle N\left( t \right) =-20{ \left( t-5 \right)  }^{ 2 }+500for\quad 0\le t\le 10$ . According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?

  1. $5:30$
  2. $7:00$
  3. $7:30$
  4. $8:00$
  5. $9:00$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given
$N(t)=-20{ (t-5) }^{ 2 }+500\quad 0\le t\le 10$
where $N(t)$ is the depth in cm in time t for maximum depth,
$\cfrac { dN }{ dt } =-20\times 2\left( t-5 \right) =0$
$t=5$
$\cfrac { { d }^{ 2 }N }{ d{ t }^{ 2 } } =-40$ (negative)
Thus at $t=5$ hours , depth will be maximum.
The water tank starts filling at $2:00$ in morning.
Therefore maximum depth$=2:00+5$ hours
$=7:00$am (hours)
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A cistern $6$ m long and $4$ m wide contains water to a depth of $1.25$ m. What is the area of wetted surface?

  1. $40$ sq. m
  2. $45$ sq. m
  3. $49$ sq. m
  4. $73$ sq. m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, $l = 6, b = 4$

Also given depth i.e., $ h = 1.25$
Area of the wetted surface $= 2[lb + bh + hl]$
$=2[(6\times 4)+(4\times 1.25)+(1.25\times 6)]$
$=2[24+5+7.5]$
$= 73$ sq. m
Therefore, the area of wetted surface is $73$ sq. m.

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

A test-tube consists of a hollow cylindrical tube joined to a hemi-spherical bown of the same internal radius. The whole tube holds $350$ cc of water and in the cylindrical portion falls $1$ cm if $19.64$ cc of water is removed. Find the length of the cylindrical portion of the tube. (Take $\pi =$ $22/7$)

  1. $12.15$ cm
  2. $16.15 $ cm
  3. $24.15 $ cm

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

Let r cm. be the radius of the hemisphere and h cm be the length of the cylindrical portion.
Volume of water removed $\pi r^2 (1) = 19.64cc$
$\Rightarrow r^2 = 19.64 \times \displaystyle \frac{7}{22}  \Rightarrow r = 2.5 cm$
Volume of the whole tube $= \pi r^2 h + \displaystyle \frac{2}{h} \pi r^3 = 350 c.c.$
$\Rightarrow \pi r^2 \displaystyle \left ( h + \frac{2}{3} r \right ) = 350$
$\Rightarrow \displaystyle \frac{22}{7} \times 2.5^2 \times \left ( h + \frac{2}{3} \times 2.5 \right ) = 350$
$\displaystyle \frac{22}{7} \times 6.25 \times (h+ 1.67) = 350 $
$ \Rightarrow \displaystyle 350 \times \frac{7}{22} \times 6. 25 - 1.67 cm    \Rightarrow h = 16.15 cm$

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

A barometric liquid having high density produces a shorter column of liquid.

  1. True

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

 pressure = $\rho$gh 

pressure remains constant so as $\rho$ will increase height will be shortened to get the same pressure .
so given statement is true , hence option (A) is correct

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

A barometer reads mercury level of $72\ cm$ at a location above sea level. If someone turns barometer  tube by $37^{o}$ with vertical, find the new reading of barometer.

  1. $76\ cm$
  2. $72\ cm$
  3. $90\ cm$
  4. $68\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The vertical height of the mercury column in a barometer is independent of the tube's inclination. If the vertical height is 72 cm, tilting the tube by 37 degrees means the length of the mercury column along the tube will be L = 72 / cos(37). Since cos(37) is approximately 0.8, L = 72 / 0.8 = 90 cm.

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

The reading of a barometer containing some air above the mercury column is 73cm while that of a correct one is 76 cm. If the tube of the faulty barometer is pushed down into mercury until volume of air in it is reduced to half, the reading shown by it will be 

  1. 70 CM

  2. 72 CM

  3. 74 CM

  4. 76 CM
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a faulty barometer with trapped air, the pressure at the mercury surface is P_atm = P_air + P_Hg. Using Boyle's law (P1V1 = P2V2) for the trapped air, where the volume is halved, the pressure of the air doubles. Solving the system of equations leads to the new reading of 70 cm.

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

To construct a barometer, a tube of length $1 m$ filled completely with mercury and is inverted in a mercury cup. The barometer reading on a particular day is $76\ cm$. Suppose a $1 m$ tube is filled with mercury up to $76\ cm$ and then closed by a cork. It is inverted in a mercury column in the tube over the surface in the cup will be

  1. Zero
  2. $76\ cm$
  3. $> 76\ cm$
  4. $< 76\ cm.$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The tube contains air $($because it is not fully filled$).$ This air pressure against atmosphere pressure$,$ 

therefore$,$ height of column $<76cm$ 
Hence,
option $(D)$ is correct answer.

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density = 13.6 gm/ $cm^3$). Using the straw, he can drink water from a glass up to a maximum depth of

  1. 10 cm

  2. 75 cm

  3. 13.6 cm

  4. 1.36 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The pressure difference between the atmosphere and the lungs supports a column of water. The pressure difference is 10 mm Hg, which is equivalent to 1 cm of Hg. Using P = h_w * d_w * g = h_Hg * d_Hg * g, the height of the water column is 13.6 cm.

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

Water barometer is possible provided barometer tube is _____$m$ long.

  1. $1$
  2. $3$
  3. $5$
  4. $11$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If water would be used in barometer, barometer tube should have the huge height of $10.3m$ Mercury is $13.6$ times more dense than water and a column weight of only $760 mm$ of Hg equals the forces generated by atmospheric pressure, so the tube can be much shorter.

Mercury is more dense. Its relative density is $13.534$ times that of water. So, to measure the atmospheric pressure, which is $760 mm$ of mercury you need a barometer ,with mercury, of length slightly more than $0.76 m$, say one meter to cover the special cases of some higher pressure. If you use water, you have to have the length of barometer of length (or height)  $13.534$ times the length of mercury barometer, which may be more than $11 m$ in length. Further mercury, being a metal has the shining quality which highlight its reading clear. Also mercury, having comparatively lower specific heat and good conductor of heat, could come to the same temperature of the atmosphere more quickly.

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

The weight of the column of the mercury in the tube above the surface of the mercury in the cup is balanced by

  1. The weight of air column

  2. Friction Force

  3. Viscous Force

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

Answer is A

The weight of mercury column is balanced by air weight and the weight of mercury column is used to calculate the pressure. 

Multiple choice physics pressure in liquids and gases common consequences of the atmospheric pressure atmospheric pressure and its consequences important points about atmospheric pressure

Siphon will fail to work if

  1. the densities of the liquid in the two vessels are equal

  2. the level of the liquid in the two vessels are at the same height

  3. both its limbs are of unequal length

  4. the temperature of the liquids in the two vessels are the same
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A siphon works based on the pressure difference created by the difference in liquid levels between two vessels. If the levels are at the same height, there is no pressure difference to drive the flow.

Multiple choice physics universe and space heliocentric model introduction to gravitation introduction to gravity

A cylinderical vessel is filled with equal amount of weight of mercury and water.The overall height of the two layer is 29.2 cm,specific gravity of mercury is 13.6.Then the pressure of the liquid at the bottom of the vessel is:

  1. $29.2 cm$ of water
  2. $\dfrac{29.2}{13.6} cm$ of mercury
  3. $4 cm$ of mercury
  4. $15.6 cm$ of mercury
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
${ M } _{ Hg }={ M } _{ w }$
${ P } _{ Hg }\left( A\times { L } _{ Hg } \right) ={ P } _{ w }\left( A\times { L } _{ w } \right) $
$\therefore$   ${ L } _{ w }=13.6{ L } _{ Hg }$
${ L } _{ w }+{ L } _{ Hg }=29.2$
$\Rightarrow { L } _{ Hg }=2cm\quad \quad { L } _{ w }=27.2cm=2cm$ of $Hg$
Total pressure $=4cm$ of $Hg$.
Multiple choice physics simple harmonic motion a few applications of linear shm simple pendulum example of simple harmonic motion

Assertion (A): A wooden cube of side a floats in a non viscous liquid of density r. When it is slightly pressed and released, then it executes SHM
Reason (R): The net force responsible for SHM is the resultant of buoyancy force and true weight of the body.

  1. Both A and R are true and R is the correct explanation of A

  2. Both A and R are true and R is not the correct explanation of A

  3. A is true and R is false

  4. A is false and R is true
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a wooden cube of side a floats in a non viscous liquid of density r and if it is slightly pressed and released it executes SHM because of the buoyancy force which is acting on the cube in upward direction. And hence the answer.