The SI unit of pressure gradient is

Options

A. `Nm^(-2)`
B. `Nm`
C. `Nm^(-1)`
D. `Nm^(-3)`

Explanation

To find the SI unit of pressure gradient, we can follow these steps:

### Step 1: Understand the Definition of Pressure Gradient
The pressure gradient is defined as the change in pressure per unit distance. Mathematically, it can be expressed as:
\[ \text{Pressure Gradient} = \frac{\Delta P}{\Delta x} \]
where \(\Delta P\) is the change in pressure and \(\Delta x\) is the change in distance.

### Step 2: Identify the SI Units of Pressure and Length
1. **Pressure (P)**: The SI unit of pressure is Pascal (Pa), which is defined as one Newton per square meter (N/m²).
2. **Length (x)**: The SI unit of length is meter (m).

### Step 3: Substitute the Units into the Pressure Gradient Formula
Using the definition of pressure gradient, we can substitute the SI units:
\[ \text{Pressure Gradient} = \frac{\text{Pressure}}{\text{Length}} = \frac{\text{N/m}^2}{\text{m}} \]

### Step 4: Simplify the Expression
Now, we simplify the expression:
\[ \text{Pressure Gradient} = \frac{\text{N/m}^2}{\text{m}} = \frac{\text{N}}{\text{m}^2} \cdot \frac{1}{\text{m}} = \frac{\text{N}}{\text{m}^3} \]

### Step 5: Conclusion
Thus, the SI unit of pressure gradient is:
\[ \text{N/m}^3 \]

### Final Answer
The correct option is **Newton per meter cubed (N/m³)**.

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