What is `SI` unit of viscosity coefficient `(eta)` ?

Options

A. Pascal
B. `Nsm^(-2)`
C. `Km^(-2)s`
D. `Nm^(-2)`

Explanation

To determine the SI unit of the viscosity coefficient (η), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Viscosity**:
Viscosity (η) is defined as the ratio of tangential force (F) to the product of the area (A) and the velocity (v) of the fluid. The formula can be expressed as:
\[ \eta = \frac{F}{A \cdot v} \]

2. **Identify the SI Units of Each Quantity**:
- **Force (F)**: The SI unit of force is Newton (N).
- **Area (A)**: The SI unit of area is square meters (m²).
- **Velocity (v)**: The SI unit of velocity is meters per second (m/s).

3. **Substitute the SI Units into the Viscosity Formula**:
Now, substituting the SI units into the formula for viscosity:
\[ \eta = \frac{N}{m² \cdot (m/s)} \]

4. **Simplify the Expression**:
When we simplify the expression, we can rewrite it as:
\[ \eta = \frac{N \cdot s}{m³} \]
Here, we multiply the numerator by seconds (s) from the velocity unit.

5. **Express Newton in Base SI Units**:
Recall that 1 Newton (N) is equivalent to \(1 \, kg \cdot m/s²\). Therefore, we can substitute this into our equation:
\[ \eta = \frac{kg \cdot m/s² \cdot s}{m³} \]

6. **Final Simplification**:
Simplifying further, we get:
\[ \eta = \frac{kg \cdot m}{m³ \cdot s} = \frac{kg}{m \cdot s} \]

7. **Express the Final SI Unit**:
The SI unit of viscosity coefficient (η) can thus be expressed as:
\[ \text{SI unit of viscosity coefficient} = \text{Pascal second (Pa·s)} = \text{Newton second per square meter (N·s/m²)} \]

### Conclusion:
The SI unit of the viscosity coefficient (η) is \( \text{N·s/m²} \) or \( \text{Pa·s} \).

---