Assertion: Reynolds number determines the nature of flow of a liquid through a pipe.
Reason: For streamlined flow, the critical velocity should be as small as possible.

Options

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

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states: "Reynolds number determines the nature of flow of a liquid through a pipe."

- **Explanation**: The Reynolds number (Re) is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is calculated using the formula:

\[ Re = \frac{\text{Inertial forces}}{\text{Viscous forces}} = \frac{\rho v D}{\mu} \]

where:
- \( \rho \) is the fluid density,
- \( v \) is the flow velocity,
- \( D \) is the characteristic length (like diameter of the pipe),
- \( \mu \) is the dynamic viscosity of the fluid.

- If \( Re < 2000 \), the flow is generally laminar (smooth and orderly).
- If \( Re > 4000 \), the flow is turbulent (chaotic and irregular).
- Thus, the assertion is **correct**.

### Step 2: Understand the Reason
The reason states: "For streamlined flow, the critical velocity should be as small as possible."

- **Explanation**: Critical velocity is the velocity above which the flow transitions from laminar to turbulent. A higher critical velocity means that the flow can remain laminar for a longer period before becoming turbulent. Therefore, for streamlined (laminar) flow, we want the critical velocity to be **high**, not low.

- Thus, the reason is **incorrect**.

### Conclusion
Since the assertion is correct and the reason is incorrect, the correct answer to the question is option **C**: "Assertion is correct. Reason is incorrect."

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