To solve these questions, we need to use the formula for the Reynolds number ($Re$):

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

Where:

• $v$ is the velocity of the fluid (in m/s),
• $D$ is the diameter of the pipe (in meters),
• $\rho$ is the density of the fluid (in kg/m³),
• $\mu$ is the dynamic viscosity of the fluid (in Pa·s or N·s/m²).

Alternatively, since dynamic viscosity $\mu$ can be written as $\mu = \nu \rho$, we can also use the form:

$Re = \frac{{v D}}{{\nu}}$

Where:

• $\nu$ is the kinematic viscosity (in m²/s).

For water at 16 °C, the following properties are typically used:

• Kinematic viscosity $\nu = 1.11 \times 10^{-6}$ m²/s.

Let's calculate part (a) first:

Part (a):

Given:

• $v = 0.9$ m/s (flow velocity),
• $D = 310$ mm = 0.310 m (pipe diameter),
• Kinematic viscosity of water, $\nu = 1.11 \times 10^{-6}$ m²/s.

Using the formula for Reynolds number:

$Re = \frac{v D}{\nu} = \frac{0.9 \times 0.310}{1.11 \times 10^{-6}}$

Let me calculate the result.The Reynolds number for water at 16 °C is approximately $251351.4$.

Since this value is much greater than 4000, the flow is considered C turbulent.

Part (b):

For heavy fuel oil with a kinematic viscosity of $\nu = 205 \, \text{mm}^2/\text{s} = 205 \times 10^{-6} \, \text{m}^2/\text{s}$, the same formula applies:

$Re = \frac{v D}{\nu}$

Let me calculate the Reynolds number for the heavy fuel oil.The Reynolds number for heavy fuel oil is approximately $1361.0$.

Since this value is less than 2000, the flow is considered A Laminar.

Summary of answers:

• Part (a):

  • $Re = 251351.4$
  • Flow type: C Turbulent

• Part (b):

  • $Re = 1361.0$
  • Flow type: A Laminar

Would you like further details on the calculation or have any other questions?

Here are some related questions:

1. What factors influence the Reynolds number besides velocity and viscosity?
2. How would increasing the pipe diameter affect the Reynolds number?
3. What is the difference between laminar and turbulent flow in practical terms?
4. How does temperature affect the viscosity and thus the Reynolds number of a fluid?
5. What are some real-world examples where knowing the flow type (laminar vs. turbulent) is crucial?

Tip: When the Reynolds number is in the transition zone (2000-4000), the flow could fluctuate between laminar and turbulent, depending on external conditions like pipe roughness.