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A trough contains mercury to a depth of 3.6 cm. If same amount of mercury is poured in it then height of mercury in the trough will be

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Important Questions on Fluid Mechanics

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The pressure at the bottom of a tank of liquid is not proportional to

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The pressure at the bottom of a liquid tank is not proportional to the

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The liquid shown in the figure in the two arms is mercury (specific gravity $13.6$ ) and water. If the difference of heights of the mercury column is $2 cm$ , the height $h$ of the water column is

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is

5 cm

and its rotational speed is

2

rotations per second, then the difference in the heights between the center and the sides, in

cm,

will be:

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A tall tank filled with water has an irregular shape as shown. The wall,

C D

makes an angle of,

45^{o}

with the horizontal; the wall,

A B

is normal to the base,

B C

. The lengths,

A B

and,

C D

are much smaller than the height,

h

of water (figure not to scale).
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Let

P_{1}, P_{2}

and

P_{3}

be the pressures exerted by the water on the wall

A B

, base

B C

, and the wall

C D

, respectively. The density of water is,

ρ

and,

g

is the acceleration due to gravity. Then, approximately

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

Two non-mixing liquids of densities

ρ

and

n ρ (n > 1)

are put in a container. The height of each liquid is

h.

A solid cylinder of length

L

and density

d

is put in this container. The cylinder floats with its axis vertical and length

p L (p < 1)

in the denser liquid. The density

d

is equal to:

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The pressure acting on a submarine is

3 \times 10^{5} Pa

at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is

1 \times 10^{5} Pa

density of water is

10^{3} kg m^{- 3}, g = 10 {ms}^{- 2}

)

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The approximate depth of an ocean is

2700 m

. The compressibility of water is

45.4 \times 10^{- 11} P a^{- 1}

and density of water is

10^{3}

{kg/m}^{3}

. What fractional compression of water will be obtained at the bottom of the ocean ?

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90^o angle at centre. Radius joining their interface makes an angle

α

with vertical. Ratio

\frac{d_{1}}{d_{2}}

is:

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

One ton stone is put on a larger piston of diameter

40 cm

of a hydraulic lift and a pressure

P

has to be applied on the smaller piston of diameter

2 cm

, to lift the stone. The pressure

P

, is approximately

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A uniform cylinder of length

L

and mass

M

having cross-sectional area

A

is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density

σ

at equilibrium position. The extension

x_{0}

of the spring when it is in equilibrium is :

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

The dimensions for pressure is

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A cylindrical block of wood (density = $650 kg m^{- 3}$ ), of base area $30 {cm}^{2}$ and height $54 cm$ , floats in a liquid of density $900 kg m^{- 3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A long container has a square base of side

L

. The height to which water should be filled so that the force on one of its side surface is the same as that at its bottom is (ignore atmospheric pressure)

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A body of density

ρ

and volume

V

is lifted through height

h

in a liquid of density

σ (< ρ) .

The increase in potential energy of the body is

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

A submarine experiences a pressure of

5.05 \times 10^{6} P a

at a depth of

d_{1}

in a sea. When it goes further to a depth of

d_{2}

, it experiences a pressure of

8.08 \times 10^{6} P a

. Then

d_{2} - d_{1}

is approximately (density of water

= 10^{3} k g / m^{3}

and acceleration due to gravity

= 10 m s^{- 2}

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

U

tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of

10 mm

above the water level on the other side. Meanwhile, the water rises by

65 mm

from its original level (see diagram). The density of the oil is ____

(ρ_{w} = 1000 kg m^{- 3})

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Physics>Mechanics>Fluid Mechanics>Pressure in a Fluid

Water stands upto height $' h'$ behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is $' ρ'$ and acceleration due to gravity is $' g'$ . If atmospheric pressure force is also considered, the point of application of total force acting on the dam due to water above $' o'$ is_____

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