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A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.

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Important Questions on Fluid Motion

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

A small spherical body of radius $r$ and density $ρ$ moves with the terminal velocity $v$ in a fluid of coefficient of viscosity $η$ and density $σ .$ What will be the net force on the body?

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

In an experiment to verify Stokes law, a small spherical ball of radius

r

and density

ρ

falls under gravity through a distance

h

in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of

h

is proportional to: (ignore viscosity of air)

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Two rain drops falling through air have radii in the ratio

1 : 2

. They will have terminal velocity in the ratio

HARD

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Water from a pipe is coming at a rate of

100

liters per minute. If the radius of the pipe is

5 c m,

the Reynolds number for the flow is of the order of: (density of water =

100 k g / m^{3},

coefficient of viscosity of water

= 1 m P a s)

HARD

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Two tubes of radii

r_{1}

and

r_{2}

and lengths

l_{1}

and

l_{2,}

respectively, are connected in series and a liquid flows through each of them in stream line conditions.

P_{1}

and

P_{2}

are pressure differences across the two tubes. If

P_{2}

4 P_{1}

and

l_{2}

\frac{l_{1}}{4}

then the radius

r_{2}

will be equal to :

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Which of the following diagrams correctly shows the relation between the terminal velocity

v_{T}

of a spherical body falling in a liquid and viscosity

η

of the liquid?

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

A rain drop of radius

0.3 mm

has a terminal velocity in air of

1 m s^{- 1}

. The viscosity of air is

8 \times 10^{- 5}

poise. The viscous force on it is

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

A small sphere of radius

r

falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains terminal velocity, is proportional to

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Which of the following option correctly describes the variation of the speed

υ

and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force

F = - k υ

, where 'k' is a constant, on the body? (Graphs are schematic and not drown to scale)

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Eight drops of water, each of radius

2 m m

are falling through air at a terminal velocity of

8 c m s^{- 1}

. If they coalesce to from a single drop, then the terminal velocity of combined drop will be:

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Two solid spheres of the same metal but of mass

M

and

8 M

fall simultaneously in a viscous liquid. The ratio of terminal velocity of the second sphere to that of the first sphere is

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

Identify the incorrect statement regarding Reynold's number

(R_{e}) :

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

The velocity of rain drop having radius

1 mm

20 cm s^{- 1}

. The velocity of raindrops of size

3 mm

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

What will be the approximate terminal velocity of a rain drop of diameter

1.8 \times 10^{- 3} m

, when density of rain water

\approx 10^{3} {kgm}^{- 3}

and the coefficient of viscosity of air

\approx 1.8 \times 10^{- 5} N - sm

^{- 2} ?

(Neglect buoyancy of air)

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

A solid sphere, of radius R acquires a terminal velocity

v_{1}

when falling (due to gravity) through a viscous fluid having a coefficient of viscosity

η .

The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity,

v_{2},

when falling through the same fluid, the ratio

(\frac{v_{1}}{v_{2}})

equals:

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

If dimensions of critical velocity,

v_{c}

of a liquid flowing through a tube are expressed as

[η^{x} ρ^{y} r^{z}]

, where,

η, ρ

and

r

are the coefficient of viscosity of liquid, density of liquid and radius of the tube, respectively, then, the values of

x

y

and

z

are given by

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter

\frac{2}{\sqrt{π}} c m

then the Reynolds number for the flow is (density of water =

10^{3} k g / m^{3} a n d v i s c o s i t y o f w a t e r = 10^{- 3} P a . s

) close to:

EASY

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

A horizontal pipeline carrying gasoline has a cross-sectional diameter of

5 mm .

If the viscosity and density of the gasoline are

6 \times 10^{- 3}

poise and

720 kg m^{- 3}

respectively, the velocity after which the flow becomes turbulent is

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

The water flows from a tap of diameter

1.25 cm

with a rate of

5 \times 10^{- 5} m^{3} s^{- 1} .

The density and coefficient of viscosity of water are

10^{3} k {gm}^{- 3}

and

10^{- 3} Pa . s

respectively. The flow of water is

HARD

Physics>Mechanical Properties of Matter>Fluid Motion>Stoke's Law and Terminal Velocity

How does Reynolds number distinguish between laminar flow and turbulent flow?

A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel.

Important Questions on Fluid Motion

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