Question

If fanning friction factor is f then the Blasius (or) Darcy friction factor is ______

• A. 4f
• B. 3f/4
• C. f/4
• D. 4f/3

Hint:

In chemical engineering literature (such as McCabe-Smith), the Fanning friction factor is typically used.
In civil and mechanical engineering literature, the Darcy friction factor is standard.
Always verify which factor is used in a given formula by checking if the constant is 16 or 64 for laminar flow (\( f = 16/Re \) vs \( f_D = 64/Re \)).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the relationship between the Fanning friction factor (\( f \)) and the Darcy-Weisbach (or Blasius) friction factor (\( f_D \)).
This is a standard fluid mechanics question related to pressure drop in pipes.

Step 2: Key Formula or Approach:
The Fanning friction factor is defined based on wall shear stress (\( \tau_w \)):
\[ f = \frac{\tau_w}{\frac{1}{2}\rho v^2} \]
The Darcy friction factor is defined based on the head loss equation:
\[ h_f = f_D \cdot \frac{L}{D} \cdot \frac{v^2}{2g} \]
Comparing the pressure drop expressions derived from both friction factors reveals their relationship.

Step 3: Detailed Explanation:

• The pressure drop \( \Delta P \) using Fanning's friction factor is:
\[ \Delta P = 4 \cdot f \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{\rho v^2}{2}\right) \]

• The pressure drop \( \Delta P \) using Darcy's friction factor is:
\[ \Delta P = f_D \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{\rho v^2}{2}\right) \]

• Equating these two expressions for the same physical system:
\[ 4 \cdot f \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{\rho v^2}{2}\right) = f_D \cdot \left(\frac{L}{D}\right) \cdot \left(\frac{\rho v^2}{2}\right) \]

• Simplify the equation:
\[ f_D = 4 \cdot f \]

• Thus, the Darcy friction factor is exactly four times the Fanning friction factor.


Step 4: Final Answer:
The Blasius (or Darcy) friction factor is equal to 4f.