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 first need to understand the concept of Reynolds number and its implications for fluid flow.

### Step-by-Step Solution:

1. **Definition of Reynolds Number**:
The Reynolds number \( R_e \) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined as:
\[ R_e = \frac{\rho v D}{\mu} \]
where:
- \( \rho \) = density of the fluid
- \( v \) = velocity of the fluid
- \( D \) = characteristic length (such as diameter of a pipe)
- \( \mu \) = dynamic viscosity of the fluid

2. **Understanding Flow Types**:
- When \( R_e < 2000 \): The flow is generally considered to be laminar. In laminar flow, fluid moves in parallel layers with minimal disruption between them.
- When \( 2000 < R_e < 4000 \): The flow is in a transitional state, where it can switch between laminar and turbulent flow.
- When \( R_e > 4000 \): The flow is considered turbulent, characterized by chaotic property changes and mixing.

3. **Analyzing the Options**:
Since the question asks for the incorrect statement regarding Reynolds number, we need to evaluate the provided options based on the standard definitions and implications of Reynolds number.

4. **Identifying the Incorrect Statement**:
- If an option states that "for \( R_e < 2000 \), the flow is turbulent", this would be incorrect because flow is laminar in this range.
- If an option states "for \( R_e > 4000 \), the flow is laminar", this would also be incorrect as flow is turbulent in this range.

5. **Conclusion**:
After analyzing the statements, we can conclude which one is incorrect based on the definitions and ranges of Reynolds number.

### Final Answer:
The incorrect statement regarding Reynolds number is that "for \( R_e < 2000 \), the flow is turbulent."