Streamline flow is more likely for liquid with

Options

A. high density and high viscosity
B. low density and low viscosity
C. high density and low viscosity
D. low density and high viscosity

Explanation

To determine the conditions under which streamline flow is more likely for liquids, we need to analyze the concept of 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 (such as diameter of a pipe)
- \(\mu\) = dynamic viscosity of the fluid

### Step-by-Step Solution:

1. **Understanding Streamline Flow**:
- Streamline flow, also known as laminar flow, occurs when the fluid flows in parallel layers with minimal disruption between them. In this type of flow, the velocity of the fluid at any given point remains constant over time.

2. **Reynolds Number and Flow Type**:
- The Reynolds number helps predict the flow regime. A low Reynolds number (typically Re < 2000) indicates laminar flow, while a high Reynolds number (Re > 4000) indicates turbulent flow. Therefore, for streamline flow to occur, we want the Reynolds number to be low.

3. **Analyzing the Components of Reynolds Number**:
- From the formula \(Re = \frac{\rho V d}{\mu}\), we can see that:
- Increasing density (\(\rho\)) or velocity (\(V\)) or characteristic length (\(d\)) will increase the Reynolds number.
- Increasing viscosity (\(\mu\)) will decrease the Reynolds number.

4. **Evaluating the Options**:
- **Option A**: High Density - This will increase the Reynolds number, making turbulent flow more likely. (Not favorable)
- **Option B**: Low Density - This will decrease the Reynolds number, but if viscosity is low, it can still lead to a higher Reynolds number. (Not favorable)
- **Option C**: High Density and Low Viscosity - High density increases Reynolds number, and low viscosity also increases it. (Not favorable)
- **Option D**: Low Density and Low Viscosity - Low density decreases the Reynolds number, and low viscosity also decreases it. This combination is favorable for achieving streamline flow.

5. **Conclusion**:
- The best conditions for streamline flow are found in **Option D: Low Density and Low Viscosity**.

### Final Answer:
Streamline flow is more likely for liquids with **Low Density and Low Viscosity**.