The unit of dynamic viscosity isa)Metre2/Secb)Metre/Secc)Pa * Secd)Dim...
Explanation: The dynamic viscosity is the ratio of shear stress to velocity gradient. Its unit is Pa * Sec.
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The unit of dynamic viscosity isa)Metre2/Secb)Metre/Secc)Pa * Secd)Dim...
The unit of dynamic viscosity is Pa * Sec, which stands for Pascal-second. Dynamic viscosity is a measure of the resistance to flow exhibited by fluids, and it is an important property in fluid mechanics. It quantifies the internal friction within a fluid when subjected to shear stress.
To understand why the correct answer is option 'C', let's break down the different units and their meanings:
1. Pascal (Pa): Pascal is the SI unit of pressure. It is defined as the force per unit area. In the context of dynamic viscosity, Pascal represents the shear stress applied to the fluid.
2. Second (Sec): Second is the SI unit of time. It represents the duration of time during which the shear stress is applied to the fluid.
Now, let's understand the concept of dynamic viscosity and how it relates to the given unit:
1. Dynamic Viscosity: Dynamic viscosity, denoted by the symbol η (eta), is a measure of a fluid's resistance to flow under an applied shear stress. It describes the internal friction between adjacent layers of fluid as they move relative to each other.
2. Shear Stress: Shear stress is the force per unit area acting parallel to a surface. In the context of fluid flow, it is the force required to maintain a constant velocity gradient or shear rate between adjacent layers of fluid.
3. Newton's Law of Viscosity: Dynamic viscosity is defined by Newton's Law of Viscosity, which states that the shear stress is directly proportional to the velocity gradient or shear rate. The proportionality constant is the dynamic viscosity.
Mathematically, dynamic viscosity (η) is given by the equation:
η = Shear Stress / Shear Rate
In SI units, the formula becomes:
η (Pa * Sec) = Shear Stress (Pa) / Shear Rate (1/Sec)
Hence, the unit of dynamic viscosity is Pascal-second (Pa * Sec), which represents the ratio of shear stress to shear rate. This unit is a measure of the internal friction within a fluid and is widely used in fluid dynamics, especially in fields like chemical engineering, where the behavior of fluids is of utmost importance.