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Which of the following is correct?
- a)Dimension of ‘dynamic viscosity’ is given by MLT-2
- b)1.0 Poise = 10.0 N-s/m2
- c)Dimension of ‘dynamic viscosity’ is given by ML-1T-1
- d)1.0 stoke = 0.001 m2/s
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is correct?a)Dimension of ‘dynamic viscos...
According to Newton's law of viscosity, shear stress is directly proportional to the rate of angular deformation (shear strain) or velocity gradient across the flow.
where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear-strain).
Units of Dynamic viscosity:
∴ the unit of dynamic viscosity in the SI unit is Ns/m2 or Pa-s.
The dimension of dynamic viscosity is ML-1T-1.
1 Pa-s = 10 Poise
∴ 1 Poise = 0.1 Pa-s or Ns/m2
Kinematic viscosity:
It is defined as the ratio between the dynamic viscosity and density of the fluid.
v = μ/ρ
Units of kinematic viscosity:
∴ the SI unit of kinematic viscosity is m2/s and the CGS unit of kinematic viscosity is cm2/s or 'Stoke'.
1 Stoke = 10-4 m2/s = 0.0001 m2/s.
The dimensional formula for Kinematic viscosity (ν) is ν = L2T-1.
where, τ = shear stress, μ = absolute or dynamic viscosity, du/dy = velocity gradient ⇒ dα/dt = rate of angular deformation (shear-strain).
Units of Dynamic viscosity:
∴ the unit of dynamic viscosity in the SI unit is Ns/m2 or Pa-s.
The dimension of dynamic viscosity is ML-1T-1.
1 Pa-s = 10 Poise
∴ 1 Poise = 0.1 Pa-s or Ns/m2
Kinematic viscosity:
It is defined as the ratio between the dynamic viscosity and density of the fluid.
v = μ/ρ
Units of kinematic viscosity:
∴ the SI unit of kinematic viscosity is m2/s and the CGS unit of kinematic viscosity is cm2/s or 'Stoke'.
1 Stoke = 10-4 m2/s = 0.0001 m2/s.
The dimensional formula for Kinematic viscosity (ν) is ν = L2T-1.
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Which of the following is correct?a)Dimension of ‘dynamic viscos...
Dimension of Dynamic Viscosity:
Dynamic viscosity is a measure of a fluid's resistance to deformation under shear stress. It is the ratio of the shear stress to the velocity gradient in a fluid flow. The dimension of dynamic viscosity is an important concept in fluid mechanics.
Explanation:
- The correct dimension of dynamic viscosity is given by ML-1T-1.
- Here, M represents mass, L represents length, and T represents time.
- The dimension ML-1T-1 signifies that dynamic viscosity is measured in units of kg/(m·s) in the International System of Units (SI).
- Dynamic viscosity plays a crucial role in determining the flow behavior of fluids, such as in the study of fluid dynamics, viscosity, and friction.
- Understanding the dimension of dynamic viscosity is essential for engineers and scientists working with fluids to accurately analyze and predict fluid flow properties.
Conclusion:
It is important to remember that the dimension of dynamic viscosity is given by ML-1T-1, indicating the units of kg/(m·s). This understanding is fundamental in various applications of fluid mechanics and plays a significant role in analyzing fluid flow behavior accurately.
Dynamic viscosity is a measure of a fluid's resistance to deformation under shear stress. It is the ratio of the shear stress to the velocity gradient in a fluid flow. The dimension of dynamic viscosity is an important concept in fluid mechanics.
Explanation:
- The correct dimension of dynamic viscosity is given by ML-1T-1.
- Here, M represents mass, L represents length, and T represents time.
- The dimension ML-1T-1 signifies that dynamic viscosity is measured in units of kg/(m·s) in the International System of Units (SI).
- Dynamic viscosity plays a crucial role in determining the flow behavior of fluids, such as in the study of fluid dynamics, viscosity, and friction.
- Understanding the dimension of dynamic viscosity is essential for engineers and scientists working with fluids to accurately analyze and predict fluid flow properties.
Conclusion:
It is important to remember that the dimension of dynamic viscosity is given by ML-1T-1, indicating the units of kg/(m·s). This understanding is fundamental in various applications of fluid mechanics and plays a significant role in analyzing fluid flow behavior accurately.
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Which of the following is correct?a)Dimension of ‘dynamic viscosity’ is given by MLT-2b)1.0 Poise = 10.0 N-s/m2c)Dimension of ‘dynamic viscosity’ is given by ML-1T-1d)1.0 stoke = 0.001 m2/sCorrect answer is option 'C'. Can you explain this answer?
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