If `R_(e)` is the Reynold's number, then which of the following is incorrect

Options

A. For `R_(e)` flow is laminer
B. For `1000 lt R_(e) lt2000`, flow is steady
C. For `R_(e) gt 2000 ` flow is turbulent
D. All are incorrect

Explanation

To determine which statement about the Reynolds number \( R_e \) is incorrect, we need to understand the definitions and characteristics of flow types associated with different ranges of \( R_e \).

### Step-by-Step Solution:

1. **Understanding Reynolds Number**:
- The Reynolds number \( R_e \) is defined as:
\[ R_e = \frac{\rho v d}{\mu} \]
where:
- \( \rho \) is the density of the fluid,
- \( v \) is the velocity of the fluid,
- \( d \) is the characteristic length (usually diameter for pipes),
- \( \mu \) is the dynamic viscosity of the fluid.

2. **Flow Types Based on Reynolds Number**:
- **Laminar Flow**: Occurs when \( R_e < 1000 \). The flow is smooth and orderly.
- **Transitional Flow**: Occurs when \( 1000 < R_e < 2000 \). The flow is neither fully laminar nor fully turbulent; it can fluctuate between the two.
- **Turbulent Flow**: Occurs when \( R_e > 2000 \). The flow is chaotic and irregular.

3. **Analyzing the Statements**:
- **Option A**: "For \( R_e \) flow is laminar for \( R_e \) belongs to 1000 to 2000."
- This statement is incorrect because the flow is transitional in this range, not laminar.

- **Option B**: "Flow is steady state for \( R_e \) belongs to 1000 to 2000."
- This statement is also incorrect because the flow in this range is transitional and can be unsteady.

- **Option C**: "For \( R_e > 2000 \) flow is turbulent."
- This statement is correct as it aligns with the definition of turbulent flow.

4. **Conclusion**:
- The incorrect statements are A and B. However, since the question asks for which is incorrect and does not specify how many, we can conclude that both A and B are incorrect.

### Final Answer:
The incorrect statement is:
- "For \( R_e \) flow is laminar for \( R_e \) belongs to 1000 to 2000."