Along a streamline,

Options

A. the velocity of a fluid particle remains constant
B. the velocity of all fluid particles crossing a given position is constant
C. the velocity of all fluid particles at a given instant is constant
D. the speed of a fluid particle remains constant

Explanation

To solve the question regarding the behavior of fluid particles along a streamline, we will analyze each of the provided statements and determine their validity based on the principles of fluid dynamics.

### Step-by-Step Solution:

1. **Understanding Streamline Flow**:
- Streamline flow refers to the flow of fluid in which the fluid particles follow smooth paths or streamlines. In this type of flow, the velocity of the fluid particles can vary from one point to another along the streamline, but the flow remains steady.

**Hint**: Recall that streamline flow is characterized by smooth paths and steady conditions.

2. **Analyzing the Statements**:
- **Statement 1**: "Velocity of a fluid particle remains constant."
- This statement is incorrect. While a fluid particle may have a certain velocity at a specific point, it can change as it moves along the streamline.

**Hint**: Consider how fluid particles can change speed or direction as they flow.

- **Statement 2**: "Velocity of fluid particles crossing a given position is constant."
- This statement is correct. At any given cross-section of the streamline, all fluid particles that cross that section will have the same velocity (both magnitude and direction) at that instant.

**Hint**: Think about the principle of continuity and how it applies to fluid flow at a specific cross-section.

- **Statement 3**: "Velocity of all fluid particles at a given instant is constant."
- This statement is incorrect. Different fluid particles can have different velocities at different points along the streamline at the same instant.

**Hint**: Reflect on how fluid velocity can vary at different points in a streamline.

- **Statement 4**: "Speed of a fluid particle remains constant."
- This statement is also incorrect. Similar to statement 1, the speed of a fluid particle can change as it moves along the streamline.

**Hint**: Remember that speed can vary, especially when the cross-sectional area of the flow changes.

3. **Conclusion**:
- Based on the analysis, the only correct statement is **Statement 2**: "Velocity of fluid particles crossing a given position is constant."

### Final Answer:
The correct answer is **Statement 2**.