A river has a flow of water with a velocity of 0.2 m/s in a pipe with a diameter of 250 mm. Calculate the Reynolds number and determine if the flow is laminar or turbulent at a temperature of 20°C.

Fluid: Water (from "River")
Velocity of flow ($V$) = $0.2 \, \text{m/s}$
Pipe diameter ($D$) = $250 \, \text{mm} = 0.250 \, \text{m}$
Temperature ($T$) = $20^\circ \text{C}$

For water at $20^\circ \text{C}$, we use the following properties:
Density ($\rho$) = $998.2 \, \text{kg/m}^3$
Dynamic viscosity ($\mu$) = $1.002 \times 10^{-3} \, \text{Ns/m}^2$

The formula for the Reynolds number is:

$$Re = \frac{\rho V D}{\mu}$$

Substitute the values:

$$Re = \frac{(998.2 \, \text{kg/m}^3) \times (0.2 \, \text{m/s}) \times (0.250 \, \text{m})}{1.002 \times 10^{-3} \, \text{Ns/m}^2}$$ $$Re = \frac{49.91 \, \text{kg} \cdot \text{m}^{-1} \cdot \text{s}^{-1}}{0.001002 \, \text{Ns/m}^2}$$ $$Re \approx 49810.38$$

For flow in a pipe:

• If $Re < 2000$, the flow is laminar.
• If $2000 < Re < 4000$, the flow is transitional.
• If $Re > 4000$, the flow is turbulent.

Since $Re \approx 49810.38$, which is greater than 4000, the flow is turbulent.

The flow is turbulent.

$$\text{Turbulent}$$