Which one of the following statements regarding streamline flow is true?

Options

A. At any given point in the fluid, the velocity is constant in time.
B. Streamline flow occurs when there are sharp obstacles in the path of a fast-moving fluid
C. Streamline flow is described by Pascal's principle.
D. Streamline flow is described by Archimedes' principle.

Answer

To determine which statement regarding streamline flow is true, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Streamline Flow**:
- Streamline flow, also known as laminar flow, occurs when a fluid flows in parallel layers with no disruption between them. The flow is smooth and orderly, and the velocity of the fluid at any given point remains constant over time.

2. **Analyzing Each Option**:
- **Option A**: "At any given point in fluid, the velocity is constant in time."
- This statement is true for streamline flow. In streamline flow, the velocity at any point does not change with time, meaning that if you measure the fluid's velocity at a specific point, it will remain the same as long as the flow conditions remain unchanged.

- **Option B**: "Streamline flow occurs when there are sharp obstacles in the path of fast-moving fluid."
- This statement is false. The presence of sharp obstacles can disturb the flow, causing turbulence and making it non-laminar. Streamline flow is characterized by the absence of obstacles that disrupt the flow.

- **Option C**: "Is described by Pascal's law."
- This statement is misleading. Pascal's law pertains to the transmission of pressure in a fluid and is not a description of streamline flow. Streamline flow is not specifically described by Pascal's law.

- **Option D**: "Is described by Archimedes principle."
- This statement is also false. Archimedes' principle deals with buoyancy and the behavior of objects in a fluid, not the characteristics of streamline flow.

3. **Conclusion**:
- The only true statement regarding streamline flow is **Option A**: "At any given point in fluid, the velocity is constant in time."

### Final Answer:
**The correct statement regarding streamline flow is Option A: At any given point in fluid, the velocity is constant in time.**