Mechanical Properties of Fluids Test

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Mechanical Properties of Fluids Test - 10

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Question 1
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The velocity of efflux of a liquid through an orifice in the bottom of the tank does not depend upon:

A
size of orifice

B
height of liquid

C
acceleration due to gravity

D
density of liquid

Solution

$$P_o + \dfrac{1}{2}\rho_{bottom} v^2 = P_o +\rho_{liquid} g h$$

Velocity of efflux is independent of the size of orifice.
The density of the fluid is actually varying with depth for large heights. In such scenarios, velocity of efflux depends on the density of the liquid.
Question 2
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Directions For Questions

A hydraulic lift is used to lift a car of mass 3000 kg. The cross sectional area of the lift on which car is supported is $$5\times 10^{-2}m^2$$ and that of smaller piston is $$10^{-4} m^2$$

...view full instructions

What is a pressure on the smaller piston if both the pistons are at same horizontal level? (Take $$g=10 ms^{-2})$$

A
3 Pa

B
$$4\times 10^3 Pa$$

C
$$6\times 10^5 Pa$$

D
1000 Pa

Solution

$$Pressure=\dfrac {3000\times 10}{5\times 10^{-2}}=6\times 10^5 Pa.$$
Question 3
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In turbulent flow, the velocity of the liquid molecules in contact with the walls of the tube.

A
is zero

B
is maximum

C
is equal to critical velocity

D
may have any value

Solution

In turbulent flow, the motion of a particle after it passes a particular point may be quite different from the motion of the particle that preceded it at that point. Turbulent flow is characterized by randomness or irreproducibility of the motion of individual particles. It usually occurs in fluids moving at high speeds.
Hence the correct answer is option D.
Question 4
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Which of the following works on Pascal's law?

A
Sprayer

B
Venturimeter

C
Hydraulic lift

D
Aneroid barometer

Solution

Pascals law states that the magnitude of pressure within fluid is equal in all parts. We use this principle in hydraulic lifts where a force applied on a smaller cylinder is transmitted to lift heavy loads using larger cylinders.
Question 5
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The volume of liquid flowing per second out of an orifice at the bottom of the tank does not depend upon:

A
the density of the liquid

B
acceleration due to gravity

C
the height of the liquid above orifice

D
the area of the orifice

Solution

$$\theta =$$ Volume flow per second.
$$\theta =$$ $$v.A$$ : where $$v$$ is flow velocity
$$v =\sqrt{2gh}$$
$$\theta =A\sqrt{2gh}$$
Hence, volume of liquid flowing per second is not depend on the density of the liquid.
So, the correct option is $$(A)$$
Question 6
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Stream line motion becomes turbulent motion when the velocity of the liquid is:

A
beyond critical velocity

B
critical velocity

C
below critical velocity

D
variable velocity

Solution

In turbulent flow, the motion of a particle after it passes a particular point may be quite different from the motion of the particle that preceded it at that point. Turbulent flow is characterized by randomness or irreproducibility of the motion of individual particles. It usually occurs in fluids moving at high speeds, above a critical velocity.
Question 7
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Which of the following is a characteristic of turbulent flow?

A
velocity more than critical velocity

B
irregular flow

C
molecules crossing from one layer to the other

D
All of the above

Solution

In turbulent flow, the motion of a particle after it passes a particular point may be quite different from the motion of the particle that preceded it at that point. Turbulent flow is characterized by randomness or irreproducibility of the motion of individual particles. It usually occurs in fluids moving at high speeds, beyond a critical velocity.
Hence all the given options are correct.
Question 8
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In a laminar flow at a given point the magnitude and direction of the velocity of the fluid:

A
both are constant

B
magnitude is only constant

C
direction is only constant

D
both are not constant

Solution

In streamline flow, the motion of a particle after it passes a particular point is the same as the motion of the particle that preceded it at that point. The path that a particle takes is called a stream line. Every particle that passes any particular point will follow the stream line that goes through that point. A bundle of stream lines, like the ones here, is known as a stream tube. Fluid never crosses the surface of a stream tube.
Question 9
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The terminal velocity depends upon:

A
$$ \dfrac {1}{r}$$

B
$$ \dfrac {1}{r^2}$$

C
$$ \dfrac {1}{r^3}$$

D
$$r^2$$

Solution

Terminal velocity, $$v_T = \dfrac {2r^2g}{9\eta}(\rho -\sigma), v_T \propto r^2$$
Question 10
1 / -0

The correct formula of critical velocity $$\left(V_c \right)$$ is :

A
$$V_c = \displaystyle \dfrac {k \eta d}{r}$$

B
$$V_c = \displaystyle \dfrac {k \eta}{dr}$$

C
$$V_c = \displaystyle \dfrac {dr}{k \eta}$$

D
$$V_c = \displaystyle \dfrac {r \eta}{dk}$$

Solution

The critical velocity depends on coefficient of viscosity $$\eta$$, density of the liquid $$d$$, and radius of the tube $$r$$ as given by
$$V_c=\dfrac{k\eta}{d r} $$ where $$k$$ is the constant of proportionality.

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Mechanical Properties of Fluids Test - 10

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Mechanical Properties of Fluids Test - 10

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SHARING IS CARING

Question 1

size of orifice

height of liquid

acceleration due to gravity

density of liquid

Solution

Question 2

3 Pa

$$4\times 10^3 Pa$$

$$6\times 10^5 Pa$$

1000 Pa

Solution

Question 3

is zero

is maximum

is equal to critical velocity

may have any value

Solution

Question 4

Sprayer

Venturimeter

Hydraulic lift

Aneroid barometer

Solution

Question 5

the density of the liquid

acceleration due to gravity

the height of the liquid above orifice

the area of the orifice

Solution

Question 6

beyond critical velocity

critical velocity

below critical velocity

variable velocity

Solution

Question 7

velocity more than critical velocity

irregular flow

molecules crossing from one layer to the other

All of the above

Solution

Question 8

both are constant

magnitude is only constant

direction is only constant

both are not constant

Solution

Question 9

$$ \dfrac {1}{r}$$

$$ \dfrac {1}{r^2}$$

$$ \dfrac {1}{r^3}$$

$$r^2$$

Solution

Question 10

$$V_c = \displaystyle \dfrac {k \eta d}{r}$$

$$V_c = \displaystyle \dfrac {k \eta}{dr}$$

$$V_c = \displaystyle \dfrac {dr}{k \eta}$$

$$V_c = \displaystyle \dfrac {r \eta}{dk}$$

Solution

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