The flow rate from a tap of diameter `1.25 cm` is `3` L//min. The coefficient of viscosity of water is `10^(-3)` pa-s. Characterize the flow.

Options

A. 1. Unsteady
B. 2. Turbulent
C. 3. Laminar
D. 4. None of above

Explanation

To characterize the flow from a tap with a diameter of 1.25 cm and a flow rate of 3 L/min, we will calculate the Reynolds number (Re). The Reynolds number helps us determine whether the flow is laminar or turbulent.

### Step-by-Step Solution:

1. **Convert Flow Rate to SI Units**:
The flow rate \( Q \) is given as 3 L/min. We need to convert this to cubic meters per second (m³/s).
\[ Q = 3 \, \text{L/min} = 3 \times 10^{-3} \, \text{m}^3/\text{min} = \frac{3 \times 10^{-3}}{60} \, \text{m}^3/\text{s} = 5 \times 10^{-5} \, \text{m}^3/\text{s} \]

2. **Calculate the Cross-Sectional Area (A)**:
The diameter \( D \) of the tap is 1.25 cm, which needs to be converted to meters.
\[ D = 1.25 \, \text{cm} = 1.25 \times 10^{-2} \, \text{m} \]
The cross-sectional area \( A \) of the tap can be calculated using the formula for the area of a circle:
\[ A = \frac{\pi D^2}{4} = \frac{\pi (1.25 \times 10^{-2})^2}{4} \approx 1.227 \times 10^{-4} \, \text{m}^2 \]

3. **Calculate the Velocity (V)**:
The velocity \( V \) can be calculated using the flow rate and the area:
\[ V = \frac{Q}{A} = \frac{5 \times 10^{-5}}{1.227 \times 10^{-4}} \approx 0.407 \, \text{m/s} \]

4. **Identify the Density (\( \rho \)) and Viscosity (\( \eta \))**:
For water, the density \( \rho \) is approximately \( 1000 \, \text{kg/m}^3 \) and the viscosity \( \eta \) is given as \( 10^{-3} \, \text{Pa.s} \).

5. **Calculate the Reynolds Number (Re)**:
The Reynolds number is calculated using the formula:
\[ Re = \frac{\rho V D}{\eta} \]
Substituting the values:
\[ Re = \frac{(1000 \, \text{kg/m}^3)(0.407 \, \text{m/s})(1.25 \times 10^{-2} \, \text{m})}{10^{-3} \, \text{Pa.s}} \approx 5095 \]

6. **Characterize the Flow**:
The flow is characterized based on the value of the Reynolds number:
- If \( Re < 2000 \): Laminar flow
- If \( 2000 < Re < 4000 \): Transitional flow
- If \( Re > 4000 \): Turbulent flow

Since \( Re \approx 5095 \), which is greater than 4000, we conclude that the flow is turbulent.

### Final Answer:
The flow from the tap is characterized as **turbulent**.