Streamline flow is more likely for liquid with

Options

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

Explanation

To determine the conditions under which a liquid exhibits streamline flow, we can analyze the Reynolds number, which is a dimensionless quantity used to predict flow patterns in different fluid flow situations. Here’s a step-by-step solution to the question:

### Step 1: Understand the Reynolds Number
The Reynolds number (Re) is defined as:
\[ Re = \frac{\rho v D}{\eta} \]
where:
- \( \rho \) = density of the fluid
- \( v \) = velocity of the fluid
- \( D \) = characteristic length (for a pipe, it is the diameter)
- \( \eta \) = dynamic viscosity of the fluid

### Step 2: Identify the Flow Regimes
The flow can be classified based on the value of the Reynolds number:
- If \( Re < 2000 \), the flow is considered to be streamline (laminar).
- If \( Re > 4000 \), the flow is considered turbulent.
- If \( 2000 < Re < 4000 \), the flow is in a transitional state.

### Step 3: Analyze Conditions for Streamline Flow
For the flow to be streamline (laminar), the Reynolds number must be less than 2000. This can be achieved by manipulating the parameters in the Reynolds number equation.

### Step 4: Determine the Effects of Viscosity and Density
From the Reynolds number equation:
- **Higher viscosity (\( \eta \))**: Increases the denominator, which reduces the Reynolds number, promoting laminar flow.
- **Lower density (\( \rho \))**: Decreases the numerator, which also reduces the Reynolds number, promoting laminar flow.

### Step 5: Conclusion
To achieve streamline flow, we need:
- High viscosity (to reduce Re)
- Low density (to also reduce Re)

Thus, the liquid that is more likely to exhibit streamline flow will have high viscosity and low density.

### Final Answer
Streamline flow is more likely for liquids with **high viscosity and low density**.

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