Streamline flow is more likely for liquid with

Options

A. 1. high density and high viscosity
B. 2. low density and low viscosity
C. 3. high density and low viscosity
D. 4. low density and high viscosity

Explanation

To determine the conditions under which streamline flow is more likely for a liquid, we need to analyze the factors that influence the Reynolds number (Re). The Reynolds number is given by the formula:

\[ Re = \frac{\rho V D}{\mu} \]

Where:
- \(\rho\) = density of the fluid
- \(V\) = velocity of the fluid
- \(D\) = characteristic length (diameter of the pipe or flow channel)
- \(\mu\) = dynamic viscosity of the fluid

### Step-by-Step Solution:

1. **Understanding Streamline Flow**:
Streamline flow (or laminar flow) occurs when the Reynolds number is low (typically \(Re < 2000\)). This means that the flow is smooth and orderly.

2. **Analyzing the Options**:
We will evaluate each option in terms of how they affect the Reynolds number.

- **Option 1: High density and high viscosity**:
- Increasing both \(\rho\) and \(\mu\) would lead to an increase in the Reynolds number, making it less likely for the flow to be streamline.
- **Conclusion**: Incorrect.

- **Option 2: Low density and low viscosity**:
- While low density (\(\rho\)) favors a lower Reynolds number, low viscosity (\(\mu\)) increases the Reynolds number.
- The combined effect does not favor streamline flow.
- **Conclusion**: Incorrect.

- **Option 3: High density and low viscosity**:
- High density increases the Reynolds number, while low viscosity decreases it. However, the increase due to high density outweighs the decrease due to low viscosity.
- **Conclusion**: Incorrect.

- **Option 4: Low density and high viscosity**:
- Low density decreases the Reynolds number, and high viscosity also decreases the Reynolds number.
- Both factors favor a lower Reynolds number, making streamline flow more likely.
- **Conclusion**: Correct.

3. **Final Answer**:
The option that makes streamline flow more likely for a liquid is **Option 4: Low density and high viscosity**.