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# Fluid Mechanics MCQ – Viscosity – 1

Water flows between two plates of which the upper one is stationary and the lower one is moving with a velocity V. What will be the velocity of the fluid in contact with the upper plate?

a) V

b) N ⁄ 2

c) 2V

d) 0

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Answer: d

Explanation: According to the No-Slip condition, the relative velocity between the plate and the fluid in contact with it must be zero. Thus, the velocity of the fluid in contact with the upper plate is 0 and that with the lower plate is V.

The viscous force the relative motion between the adjacent layers of a fluid in motion.

Which one of the flowing fits best in the sentence?

a) opposes

b) never affects

c) facilitates

d) may effect under certain conditions

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Answer: a

Explanation: Viscosity is the internal friction of a fluid in motion. It is the property by the virtue of which the relative motion between two adjacent fluid layers is opposed.

The viscosity of a fluid in motion is 1 Poise. What will be it’s viscosity (in Poise) when the fluid is at rest?

a) 0

b) 0.5

c) 1

d) 2

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Answer: c

Explanation: Viscosity is the property of a fluid and is constant for a given fluid under given conditions, irrespective of the fact whether the fluid is at rest or in motion.

Which of the following correctly states how the viscosities of a liquid and a gas will change with temperature?

a) Viscosity increases with the increase in temperature of a liquid and decreases with the increase in temperature of a gas

b) Viscosity increases with the increase in temperature of a liquid and increases with the increase in temperature of a gas

c) Viscosity decreases with the increase in temperature of a liquid and decreases with the increase in temperature of a gas

d) Viscosity decreases with the increase in temperature of a liquid and increases with the increase in temperature of a gas

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Answer: a

Explanation: Viscosity of a liquid is due to the cohesion between it’s molecules. With the increase in temperature of a liquid, cohesion increases, leading to the rise in viscosity. Viscosity of a gas is due to the momentum transfer between it’s molecules. With the increase in the temperature of a liquid, molecular motion increases, leading to the fall in viscosity

Which one of the following is not a unit of dynamic viscosity?

a) Pa-s

b) N-s/m2

c) Poise

d) Stokes

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Answer: d

Explanation:

where F= viscous force, A= area, du ⁄ dx = velocity gradient, μ = co-effcient of viscosity. Therefore,

SI unit of μ is N-s/m^{2} = Pa-s and CGS unit of μ is dyne-s/cm^{2}. 1 Poise= 1 dyne-s/cm^{2} and 1 Stokes= 1 cm^{2}/s. Thus, Stokes is not an unit of μ, rather it is a unit of kinematic viscosity υ.

Which of the following is a unit of dynamic viscosity?

a) [M1 L1 T-1].

b) [M1 L-1 T-1].

c) [M1 L-2 T-2].

d) [M1 L-2 T-2].

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Answer: b

Explanation:

where F= viscous force, A= area, du ⁄ dx = velocity gradient, μ = co-effcient of viscosity. Therefore,

Which one of the following is the CGS unit of dynamic viscosity?

a) Stokes

b) Pa-s

c) m2/s

d) Poise

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Answer: d

Explanation:

where F= viscous force, A= area, du ⁄ dx = velocity gradient, μ = co-effcient of viscosity. Therefore,

CGS unit of μ is = dyne-s/cm^{2}. 1 Poise= 1 dyne-s/cm^{2} and 1 Stokes= 1 cm^{2}/s. Thus, the CGS unit of μ will be Poise. Stokes is the CGS unit of kinematic viscosity.

The dynamic viscosity of a fluid is 1 Poise. What should one multiply to it to get the answer in N-s/m2?

a) 0.1

b) 1

c) 10

d) 100

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Answer: a

Explanation:

1 Poise = 1 dyne-s/cm^{2}

Which of the following is a unit of kinematic viscosity?

a) Stokes

b) Pa-s

c) m2=s

d) Poise

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Answer: a

Explanation: ν = μ/ρ, where ν = kinematic viscosity, μ = dynamic viscosity and ρ = density of the fluid. Unit of μ is dyne-s/cm^{2} and that of ρ is kg/cm^{3}.

Thus, the unit of ν is cm^{2}/s = Stokes Poise is the unit of dynamic viscosity

1 Poise = 1 dyne-s/cm^{2}

Which of the following is the dimension of kinematic viscosity?

a) [L1 T-1].

b) [L1 T-2].

c) [L2 T-1].

d) [L2 T-2].

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Answer: c

Explanation: ν = μ/ρ, where ν = kinematic viscosity, μ = dynamic viscosity and ρ = density of the fluid

The kinematic viscosity of a fluid is 0.1 Stokes. What will be the value is m2/s?

a) 10-2

b) 10-3

c) 10-4

d) 10-5

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Answer: d

Explanation: 1Stokes = 1cm2/s = 10-4m2/s Therefore, 0.1Stokes = 10-1cm2/s = 10-5m2/s.

The shear stress at a point in a liquid is found to be 0.03 N/m2. The velocity gradient at the point is 0.15 s-1. What will be it’s viscosity (in Poise)?

a) 20

b) 2

c) 0.2

d) 0.5

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Answer: b

Explanation:

The space between two plates (20cm*20cm*1cm), 1 cm apart, is filled with a liquid of viscosity 1 Poise. The upper plate is dragged to the right with a force of 5N keeping the lower plate stationary.

What will be the velocity in m/s of flow at a point 0.5 cm below the lower surface of the upper plate if linear velocity profile is assumed for the flow?

a) 1.25

b) 2.5

c) 12.5

d) 0.25

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Answer: c

Explanation:

where F_{ν} = viscous force, A = area, du ⁄ dx = velocity gradient, μ = co-effcient of viscosity. If linear velocity profile is assumed, du⁄dx = U/x, where U = velocity of the upper plate and x = distance between the two plates. Now, the viscous force Fv = -F= -5N. Substituting all the values in the equation, U becomes 12.5 m/s.