Assertion: The flow of fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant.
Reason: The path taken by a fluid particle under a steady flow is a streamline.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true and reason is false.
D. If both assertion and reason are false.

Explanation

To analyze the given question, we will break down the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that "The flow of fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant."

- **Explanation**: In fluid mechanics, a steady flow means that the fluid's velocity at a particular point does not change over time. This means that if you were to measure the velocity of the fluid at that point at different times, you would get the same value each time.

### Step 2: Understanding the Reason
The reason states that "The path taken by a fluid particle under a steady flow is a streamline."

- **Explanation**: A streamline is a path that a fluid particle follows in a steady flow. In a steady flow, the fluid particles do not cross each other, and the streamlines represent the direction of the fluid's velocity at every point in the flow. Thus, if the flow is steady, the path taken by any fluid particle will always be along a streamline.

### Step 3: Evaluating the Relationship
Now, we need to evaluate the relationship between the assertion and the reason.

- The assertion is correct because it accurately describes steady flow.
- The reason is also correct because it correctly defines what a streamline is in the context of steady flow.

However, while both statements are true, the reason does not provide a direct explanation for the assertion. The assertion defines steady flow, while the reason describes the characteristics of the flow.

### Conclusion
Both the assertion and the reason are correct statements, but the reason does not explain the assertion. Therefore, the answer to the question is that the assertion is true, the reason is true, but the reason does not support the assertion.

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