The onset of turbulance in a liquid is determined by

Options

A. 1. Pascal's law
B. 2. Reynold's law
C. 3. Torricell's law
D. 4. Bernoulli's principle

Explanation

To determine the onset of turbulence in a liquid, we need to analyze the concept of the Reynolds number. Here’s a step-by-step solution:

### Step 1: Understand the Reynolds Number
The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined 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 in this case)
- \( \mu \) = dynamic viscosity of the fluid

### Step 2: Analyze the Flow Regimes
The value of the Reynolds number helps us categorize the flow of the fluid:
- **Laminar Flow**: When \( Re < 2100 \), the flow is smooth and orderly.
- **Transitional Flow**: When \( 2100 < Re < 4000 \), the flow is unstable and can transition between laminar and turbulent.
- **Turbulent Flow**: When \( Re > 4000 \), the flow becomes chaotic and irregular.

### Step 3: Conclusion
From the above analysis, we can conclude that the onset of turbulence in a liquid is determined by the Reynolds number. Specifically, a Reynolds number greater than 4000 indicates that the flow has transitioned to a turbulent state.

### Final Answer
The onset of turbulence in a liquid is determined by the **Reynolds number**.

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