EASY

Earn 100

Define critical velocity?

Important Questions on Mechanical Properties of Fluids

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

The velocity of water in a river is

18 km h^{- 1}

near the surface. If the river is

5 m

deep, find the shearing stress between the horizontal layers of water. The coefficient of viscosity of water

= 10^{- 2} poise

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

p

is the density and

η

is coefficient of viscosity of fluid which flows with a speed

v

in the pipe of diameter

d

, the correct formula for Reynolds number

R_{e}

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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 :

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

A steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown below. The terminal velocity of the ball is closest to

Question Image

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below:

Question Image

Artery is contracted in region $II$ . Choose the correct statement.

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is

V .

if the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Two rain drops falling through air have radii in the ratio

1 : 2

. They will have terminal velocity in the ratio

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Two capillary tubes of same length each of

50 cm

but of different radii

4 mm

and

2 mm

are connected in series. When water flows, the pressure difference between the ends of the arrangement is

P

. Then the pressure difference between the ends of the first tube is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Consider a thin square plate floating on a viscous liquid in a large tank. The height

h

of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity

u_{0}

. Which of the following statements is (are) true?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

Identify the incorrect statement regarding Reynold's number

(R_{e}) :

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Critical Velocity and Reynolds Number

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:

Define critical velocity?

Important Questions on Mechanical Properties of Fluids

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