In a streamline flow

Options

A. the speed of a particle always remains same
B. the velocity of a particle always remains same
C. the kinetic energies of all particles arriving at a given point are the same
D. the potential eneergies of all the particles arriving at a given point are the same

Explanation

To solve the question regarding streamline flow, we will analyze the properties of the flow and evaluate the given options step by step.

### Step-by-Step Solution:

1. **Understanding Streamline Flow**:
- Streamline flow refers to a type of fluid flow where the fluid moves in parallel layers with no disruption between them. The path followed by the fluid particles is called a streamline.
- In streamline flow, the velocity of the fluid particles at any point is constant over time, but it can vary from point to point.

**Hint**: Remember that streamline flow is characterized by smooth, continuous paths of fluid particles.

2. **Analyzing the Options**:
- **Option 1**: "The speed of a particle always remains the same."
- This is incorrect because while the speed can be constant along a streamline, it can vary from one streamline to another.

**Hint**: Consider that speed can change from one point to another in a fluid.

- **Option 2**: "The velocity of the particle always remains the same."
- This is also incorrect. Velocity is a vector quantity that includes both speed and direction. While the speed may be constant along a streamline, the direction can change, leading to a change in velocity.

**Hint**: Recall that velocity depends on both speed and direction.

- **Option 3**: "The kinetic energies of all particles arriving at a given point are the same."
- This is correct. In a streamline flow, the kinetic energy of fluid particles can be considered equal at a given point if they are at the same height and moving along the same streamline.

**Hint**: Kinetic energy depends on speed, and for particles at the same point in a streamline flow, their speeds can be considered equal.

- **Option 4**: "The potential energies of all particles arriving at a given point are the same."
- This is not necessarily true. The potential energy can vary based on the height of the particles in a gravitational field or other factors affecting potential energy.

**Hint**: Potential energy can change based on the position of the particles in the field.

3. **Conclusion**:
- After evaluating all the options, the correct answer is **Option 3**: "The kinetic energies of all particles arriving at a given point are the same."

### Summary:
In streamline flow, the kinetic energy of fluid particles arriving at a given point can be considered the same due to the nature of the flow, while other properties such as speed and potential energy can vary.