the flow rate of water from a tap of diameter 1.25cm is 0.48L/m.the coefficient of viscosity of water is 10^-3Pa.Charaterise the flow of liquid.

To characterize the flow of water from a tap with a diameter of 1.25 cm and a flow rate of 0.48 L/min, we need to analyze a few key concepts: the type of flow, the Reynolds number, and the implications of viscosity. Let's break this down step by step.

Understanding Flow Types

Flow can generally be classified into two categories: laminar and turbulent. Laminar flow occurs when the fluid moves in parallel layers, with minimal disruption between them. In contrast, turbulent flow is characterized by chaotic changes in pressure and velocity.

Calculating the Reynolds Number

The Reynolds number (Re) is a dimensionless quantity that helps us determine the flow regime. It is calculated using the formula:

• Re = (ρ * v * D) / μ

Where:

• ρ = density of the fluid (for water, approximately 1000 kg/m³)
• v = average velocity of the fluid (m/s)
• D = diameter of the pipe (m)
• μ = dynamic viscosity of the fluid (Pa·s)

Finding Average Velocity

First, we need to convert the flow rate from liters per minute to cubic meters per second:

• 0.48 L/min = 0.48 / 1000 m³/min = 0.00048 m³/min
• To convert to seconds: 0.00048 m³/min ÷ 60 = 0.000008 m³/s

Next, we calculate the cross-sectional area (A) of the tap:

• A = π * (D/2)² = π * (0.0125 m / 2)² ≈ 1.227 × 10^-4 m²

Now, we can find the average velocity (v):

• v = Q / A = 0.000008 m³/s / 1.227 × 10^-4 m² ≈ 0.065 m/s

Calculating the Reynolds Number

Now, substituting the values into the Reynolds number formula:

• Re = (1000 kg/m³ * 0.065 m/s * 0.0125 m) / (10^-3 Pa·s)
• Re ≈ 812.5

Interpreting the Results

The Reynolds number of approximately 812.5 indicates that the flow is likely laminar, as it is below the typical threshold of 2000 for flow transitioning to turbulence. In laminar flow, the fluid moves smoothly, and the effects of viscosity are more pronounced.

Implications of Viscosity

With a viscosity of 10^-3 Pa·s, water's resistance to flow is relatively low, which is typical for liquids. This low viscosity supports the laminar flow regime, allowing for a steady and predictable flow from the tap.

Conclusion

In summary, the flow of water from the tap can be characterized as laminar due to the calculated Reynolds number being below 2000. The low viscosity of water further supports this classification, indicating that the flow is smooth and orderly. Understanding these principles helps us appreciate the behavior of fluids in various contexts, from household plumbing to industrial applications.