Find the nature of flow of water flowing at a speed of `8 cms"^(-1)` through a horizontal tube of radius 2 cm. The viscosity of water at room temperature is 0.01 Poise.

Answer

To determine the nature of the flow of water through a horizontal tube, we need to calculate the Reynolds number (Re). The Reynolds number helps us understand whether the flow is laminar or turbulent.

### Step-by-Step Solution:

1. **Identify the given values:**
- Speed of water (v) = 8 cm/s
- Radius of the tube (r) = 2 cm
- Viscosity of water (μ) = 0.01 Poise
- Density of water (ρ) = 1 g/cm³ (since we are using CGS units)

2. **Calculate the diameter of the tube:**
\[ \text{Diameter} (D) = 2 \times \text{Radius} = 2 \times 2 \text{ cm} = 4 \text{ cm} \]

3. **Use the formula for Reynolds number:**
The formula for Reynolds number is given by:
\[ Re = \frac{\rho v D}{\mu} \]
where:
- \( \rho \) = density of the fluid (1 g/cm³)
- \( v \) = velocity of the fluid (8 cm/s)
- \( D \) = diameter of the tube (4 cm)
- \( \mu \) = viscosity of the fluid (0.01 Poise)

4. **Substitute the values into the Reynolds number formula:**
\[ Re = \frac{(1 \text{ g/cm}^3)(8 \text{ cm/s})(4 \text{ cm})}{0.01 \text{ Poise}} \]

5. **Calculate the Reynolds number:**
\[ Re = \frac{32 \text{ g/cm}^2/\text{s}}{0.01 \text{ g/cm·s}} = 3200 \]

6. **Determine the nature of the flow:**
- If \( Re < 2000 \), the flow is laminar.
- If \( 2000 < Re < 4000 \), the flow is transitional.
- If \( Re > 4000 \), the flow is turbulent.

Since we calculated \( Re = 3200 \), the flow is transitional.

### Conclusion:
The nature of the flow of water flowing at a speed of 8 cm/s through a horizontal tube of radius 2 cm is **transitional**.