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The dimension of dynamic viscosity of a fluid is:
- a)[MLT−1]
- b)[L2T−1]
- c)[LT−2]
- d)[M L-1 T-1]
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The dimension of dynamic viscosity of a fluid is:a)[MLT−1]b)[L2T−1]c)...
thus, the unit of dynamic viscosity is N−s/m2 or kg/(m.sec), and dimension is ML
−1T−1
Most Upvoted Answer
The dimension of dynamic viscosity of a fluid is:a)[MLT−1]b)[L2T−1]c)...
The dimension of dynamic viscosity of a fluid is [M L-1 T-1].
Explanation:
Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force or stress. It quantifies the internal friction within the fluid as it flows. The dimension of dynamic viscosity can be determined by analyzing the variables involved in its calculation.
The SI unit of dynamic viscosity is Pascal-second (Pa·s), but it can also be expressed in other units such as poise (P) or centipoise (cP).
Let's break down the dimensions of dynamic viscosity:
- Mass (M): The dynamic viscosity depends on the mass of the fluid. A fluid with a greater mass will generally have a higher viscosity.
- Length (L): The dynamic viscosity is influenced by the length or distance over which the fluid flows. This can be observed in the shear rate, which is the change in velocity with respect to distance.
- Time (T): The dynamic viscosity is directly related to the time it takes for the fluid to flow under a given force or stress. It represents the rate at which the fluid changes its shape due to the applied stress.
- Power of Mass (L-1): The power of mass in the dimension indicates that the dynamic viscosity is inversely proportional to mass. As the mass increases, the viscosity decreases.
- Power of Time (T-1): The power of time in the dimension indicates that the dynamic viscosity is inversely proportional to time. As the time increases, the viscosity decreases.
Therefore, combining all the dimensions, the dimension of dynamic viscosity is [M L-1 T-1]. This represents the ratio of the force or stress applied to the fluid to the rate of change of velocity with respect to distance and time.
In conclusion, option 'D' [M L-1 T-1] is the correct answer for the dimension of dynamic viscosity of a fluid.
Explanation:
Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force or stress. It quantifies the internal friction within the fluid as it flows. The dimension of dynamic viscosity can be determined by analyzing the variables involved in its calculation.
The SI unit of dynamic viscosity is Pascal-second (Pa·s), but it can also be expressed in other units such as poise (P) or centipoise (cP).
Let's break down the dimensions of dynamic viscosity:
- Mass (M): The dynamic viscosity depends on the mass of the fluid. A fluid with a greater mass will generally have a higher viscosity.
- Length (L): The dynamic viscosity is influenced by the length or distance over which the fluid flows. This can be observed in the shear rate, which is the change in velocity with respect to distance.
- Time (T): The dynamic viscosity is directly related to the time it takes for the fluid to flow under a given force or stress. It represents the rate at which the fluid changes its shape due to the applied stress.
- Power of Mass (L-1): The power of mass in the dimension indicates that the dynamic viscosity is inversely proportional to mass. As the mass increases, the viscosity decreases.
- Power of Time (T-1): The power of time in the dimension indicates that the dynamic viscosity is inversely proportional to time. As the time increases, the viscosity decreases.
Therefore, combining all the dimensions, the dimension of dynamic viscosity is [M L-1 T-1]. This represents the ratio of the force or stress applied to the fluid to the rate of change of velocity with respect to distance and time.
In conclusion, option 'D' [M L-1 T-1] is the correct answer for the dimension of dynamic viscosity of a fluid.
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The dimension of dynamic viscosity of a fluid is:a)[MLT−1]b)[L2T−1]c)[LT−2]d)[M L-1 T-1]Correct answer is option 'D'. Can you explain this answer?
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