EASY

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What is steady and unsteady flow of fluid?

Important Questions on Mechanical Properties of Fluids

HARD

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

Consider the wall of a dam to be straight with height

H

and length

L

. It holds a lake of water of height

h (h < H)

on one side. Let the density of water be

ρ_{w}

Denote the torque about the axis along the bottom length of the wall by

τ_{1}

. Denote also a similar torque due to the water up to height

\frac{h}{2}

and wall length

\frac{L}{2}

τ_{2}

. Then,

\frac{τ_{1}}{τ_{2}}

(ignore atmospheric pressure) is

MEDIUM

Physics>Mechanics>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:

HARD

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

A bubble of radius

R

in water of density

ρ

is expanding uniformly at speed

v

. Given that water is incompressible, the kinetic energy of water being pushed is

MEDIUM

Physics>Mechanics>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:

EASY

Physics>Mechanics>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}

HARD

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

Consider the configuration of a stationary water tank of cross-section area $A_{0}$ and a small bucket as shown in figure below;

Question Image

What should be the speed $v$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket?

(Take, $h = 5 m, H = 5 m, g = 10 m s^{- 2}, A = 5 {cm}^{2}$ and $A_{0} = 500 {cm}^{2}$ ).

HARD

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

Air (density

ρ

) is being blown on a soap film (surface tension

T

) by a pipe of radius

R

with its opening right next to the film. The film is deformed and a bubble detaches from the film when the shape of the deformed surface is a hemisphere. Given that the dynamic pressure on the film due to the air blown at speed

v

\frac{1}{2} ρ v^{2},

the speed at which the bubble formed is

MEDIUM

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

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 L {(\min)}^{- 1}$ to $0.48 L {(\min)}^{- 1} ?$ The radius of the tap and viscosity of water are $0.5 cm$ and $10^{- 3} Pa s$ , respectively. (Density of water : $10^{3} kg m^{- 3}$ )