09. Critical velocity and Reynolds number
Mechanical Properties of Fluids

143388 A copper ball of radius $3.0 \mathrm{~mm}$ falls in an oil tank of viscosity $1 \mathrm{~kg} / \mathrm{m}$-s. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, Density of copper $=9 \times 10^{3}$ $\mathrm{kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.)

1 $18 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
2 $25 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
3 $15 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
4 $20 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143390 The Reynold's number for a liquid flow in a tube does NOT depend on

1 the velocity of the liquid
2 the viscosity of the liquid
3 the length of the tube
4 the diameter of the tube
Mechanical Properties of Fluids

143392 A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8 \mathrm{M}$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

1 $8 \mathrm{v}$
2 $\frac{\mathrm{v}}{8}$
3 $2 \mathrm{v}$
4 $4 \mathrm{v}$
Mechanical Properties of Fluids

143393 The flow rate of water from a tap of diameter $1.25 \mathrm{~cm}$ is $\mathbf{3}$ litres per minute. If coefficient of viscosity of water is $10^{-3}$ Pa.s, the nature of flow is

1 Unsteady
2 Turbulent
3 Streamlined
4 Laminar
Mechanical Properties of Fluids

143389 Assertion: For Reynold's number $R_{e}>2000$, the flow of fluid is turbulent.
Reason: Inertial forces are dominant compared to the viscous forces at such high Reynold's numbers.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Mechanical Properties of Fluids

143388 A copper ball of radius $3.0 \mathrm{~mm}$ falls in an oil tank of viscosity $1 \mathrm{~kg} / \mathrm{m}$-s. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, Density of copper $=9 \times 10^{3}$ $\mathrm{kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.)

1 $18 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
2 $25 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
3 $15 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
4 $20 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143390 The Reynold's number for a liquid flow in a tube does NOT depend on

1 the velocity of the liquid
2 the viscosity of the liquid
3 the length of the tube
4 the diameter of the tube
Mechanical Properties of Fluids

143392 A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8 \mathrm{M}$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

1 $8 \mathrm{v}$
2 $\frac{\mathrm{v}}{8}$
3 $2 \mathrm{v}$
4 $4 \mathrm{v}$
Mechanical Properties of Fluids

143393 The flow rate of water from a tap of diameter $1.25 \mathrm{~cm}$ is $\mathbf{3}$ litres per minute. If coefficient of viscosity of water is $10^{-3}$ Pa.s, the nature of flow is

1 Unsteady
2 Turbulent
3 Streamlined
4 Laminar
Mechanical Properties of Fluids

143389 Assertion: For Reynold's number $R_{e}>2000$, the flow of fluid is turbulent.
Reason: Inertial forces are dominant compared to the viscous forces at such high Reynold's numbers.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Mechanical Properties of Fluids

143388 A copper ball of radius $3.0 \mathrm{~mm}$ falls in an oil tank of viscosity $1 \mathrm{~kg} / \mathrm{m}$-s. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, Density of copper $=9 \times 10^{3}$ $\mathrm{kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.)

1 $18 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
2 $25 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
3 $15 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
4 $20 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143390 The Reynold's number for a liquid flow in a tube does NOT depend on

1 the velocity of the liquid
2 the viscosity of the liquid
3 the length of the tube
4 the diameter of the tube
Mechanical Properties of Fluids

143392 A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8 \mathrm{M}$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

1 $8 \mathrm{v}$
2 $\frac{\mathrm{v}}{8}$
3 $2 \mathrm{v}$
4 $4 \mathrm{v}$
Mechanical Properties of Fluids

143393 The flow rate of water from a tap of diameter $1.25 \mathrm{~cm}$ is $\mathbf{3}$ litres per minute. If coefficient of viscosity of water is $10^{-3}$ Pa.s, the nature of flow is

1 Unsteady
2 Turbulent
3 Streamlined
4 Laminar
Mechanical Properties of Fluids

143389 Assertion: For Reynold's number $R_{e}>2000$, the flow of fluid is turbulent.
Reason: Inertial forces are dominant compared to the viscous forces at such high Reynold's numbers.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Mechanical Properties of Fluids

143388 A copper ball of radius $3.0 \mathrm{~mm}$ falls in an oil tank of viscosity $1 \mathrm{~kg} / \mathrm{m}$-s. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, Density of copper $=9 \times 10^{3}$ $\mathrm{kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.)

1 $18 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
2 $25 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
3 $15 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
4 $20 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143390 The Reynold's number for a liquid flow in a tube does NOT depend on

1 the velocity of the liquid
2 the viscosity of the liquid
3 the length of the tube
4 the diameter of the tube
Mechanical Properties of Fluids

143392 A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8 \mathrm{M}$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

1 $8 \mathrm{v}$
2 $\frac{\mathrm{v}}{8}$
3 $2 \mathrm{v}$
4 $4 \mathrm{v}$
Mechanical Properties of Fluids

143393 The flow rate of water from a tap of diameter $1.25 \mathrm{~cm}$ is $\mathbf{3}$ litres per minute. If coefficient of viscosity of water is $10^{-3}$ Pa.s, the nature of flow is

1 Unsteady
2 Turbulent
3 Streamlined
4 Laminar
Mechanical Properties of Fluids

143389 Assertion: For Reynold's number $R_{e}>2000$, the flow of fluid is turbulent.
Reason: Inertial forces are dominant compared to the viscous forces at such high Reynold's numbers.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Mechanical Properties of Fluids

143388 A copper ball of radius $3.0 \mathrm{~mm}$ falls in an oil tank of viscosity $1 \mathrm{~kg} / \mathrm{m}$-s. Then, the terminal velocity of the copper ball will be (Density of oil $=1.5 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$, Density of copper $=9 \times 10^{3}$ $\mathrm{kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$.)

1 $18 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
2 $25 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
3 $15 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
4 $20 \times 10^{-2} \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143390 The Reynold's number for a liquid flow in a tube does NOT depend on

1 the velocity of the liquid
2 the viscosity of the liquid
3 the length of the tube
4 the diameter of the tube
Mechanical Properties of Fluids

143392 A metallic spherical ball of mass $M$ is dropped into a liquid and after some time it reaches a terminal velocity of $v$. If another spherical ball of mass $8 \mathrm{M}$ made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

1 $8 \mathrm{v}$
2 $\frac{\mathrm{v}}{8}$
3 $2 \mathrm{v}$
4 $4 \mathrm{v}$
Mechanical Properties of Fluids

143393 The flow rate of water from a tap of diameter $1.25 \mathrm{~cm}$ is $\mathbf{3}$ litres per minute. If coefficient of viscosity of water is $10^{-3}$ Pa.s, the nature of flow is

1 Unsteady
2 Turbulent
3 Streamlined
4 Laminar
Mechanical Properties of Fluids

143389 Assertion: For Reynold's number $R_{e}>2000$, the flow of fluid is turbulent.
Reason: Inertial forces are dominant compared to the viscous forces at such high Reynold's numbers.

1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.