The SI units of the coefficient of viscosity is ………………………….. .

Answer

To determine the SI units of the coefficient of viscosity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition**: The coefficient of viscosity (often denoted by the Greek letter μ) is a measure of a fluid's resistance to flow. It quantifies how much force is needed to move one layer of fluid in relation to another.

2. **Identify the Basic Units**: Viscosity is related to force and area. The basic SI unit of force is the Newton (N), and the basic SI unit of area is square meters (m²).

3. **Relate Viscosity to Force and Area**: The coefficient of viscosity can be expressed in terms of force and area. Specifically, it can be defined as:
\[ \text{Viscosity} = \frac{\text{Force}}{\text{Area} \times \text{Velocity}} \]
Here, velocity is measured in meters per second (m/s).

4. **Substituting Units**:
- Force (N) = kg·m/s²
- Area (m²) = m²
- Velocity (m/s) = m/s

Therefore, the units of viscosity can be expressed as:
\[ \text{Viscosity} = \frac{\text{N}}{\text{m}^2 \cdot \text{m/s}} = \frac{\text{N} \cdot \text{s}}{\text{m}^2} \]

5. **Convert Newton to Pascal**: Since 1 Pascal (Pa) is defined as 1 Newton per square meter (N/m²), we can express the viscosity in terms of Pascal:
\[ \text{Viscosity} = \frac{\text{Pa} \cdot \text{s}}{1} = \text{Pa} \cdot \text{s} \]

6. **Final Units**: Thus, the SI unit of the coefficient of viscosity can be expressed as:
- Pascal second (Pa·s)
- Alternatively, it can also be expressed as Newton second per square meter (N·s/m²).

### Conclusion:
The SI units of the coefficient of viscosity are **Pascal second (Pa·s)** or **Newton second per square meter (N·s/m²)**.

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