Question

For laminar fluid flow through a smooth circular tube, the relation between friction factor (f) and Reynolds number (Re) is

• A. \( f = \frac{16}{Re} \)
• B. \( f = \frac{24}{Re} \)
• C. \( f = \frac{16}{\sqrt{Re}} \)
• D. \( f = \frac{24}{\sqrt{Re}} \)

Hint:

For fluid dynamics problems, always identify the flow regime (laminar or turbulent) using the Reynolds number. Memorize the friction factor formula for laminar flow (\(f = 16/Re\)) as it's a frequently tested concept.

Answer 1

The Correct Option is A

Step 1: Understanding the Flow Type:
The nature of fluid flow inside a pipe is determined using the Reynolds number ($Re$). For flow through a circular tube, when $Re<2100$, the flow is classified as laminar. In laminar flow, viscous forces dominate and the fluid moves in smooth, orderly layers.
Step 2: Friction Factor in Laminar Flow:
The friction factor represents the resistance offered by the pipe wall to fluid motion. In fluid mechanics, two types of friction factors are used: Fanning friction factor ($f$) and Darcy friction factor ($f_D$). The relation for laminar flow in a smooth circular pipe is derived from the Hagen–Poiseuille equation.
Step 3: Mathematical Relation:
For fully developed laminar flow in a smooth tube, the analytical solution of the Navier–Stokes equation gives: \[ f = \frac{16}{Re} \] This expression corresponds to the Fanning friction factor.
Step 4: Final Conclusion:
Since the question refers to laminar flow in a smooth circular tube, the correct relation between friction factor and Reynolds number is: \[ f = \frac{16}{Re} \]