Turbulent flow in a smooth new pipe (engineering correlations): which expression gives the Fanning friction factor f as a function of Reynolds number NRe in the range ~4×10^3 to 1×10^5?

Introduction / Context:
Pressure drop predictions in pipelines require a reliable friction factor. For smooth, new pipes with fully developed turbulent flow, empirical correlations provide quick estimates before detailed roughness-based charts (e.g., Moody) are consulted.

Given Data / Assumptions:

• Smooth, new pipe with negligible roughness.
• Fanning friction factor f is used (note: Darcy–Weisbach factor is 4f).
• Flow is fully turbulent with Reynolds number roughly between 4×10^3 and 1×10^5.

Concept / Approach:
The Blasius-type correlation for smooth pipes in terms of the Fanning factor is f = 0.079 * NRe^-0.25. A common source of confusion is the Darcy factor, which would be f_D = 0.316 * NRe^-0.25. Distinguishing which definition is used is crucial to avoid a factor-of-four error.

Step-by-Step Solution:
Identify the factor requested: Fanning friction factor f.Recall the Blasius correlation for smooth pipes: f = 0.079 * NRe^-0.25.Select the option matching this formula.

Verification / Alternative check:
Cross-check against Moody chart: for NRe = 10^5 in a smooth tube, Fanning f ≈ 0.003–0.004, consistent with 0.079 * 10^-1.25 ≈ 0.0044.

Why Other Options Are Wrong:
0.316 * NRe^-0.25: This is the Darcy factor, not the Fanning factor.0.22 * NRe^0.5: Dimensionally and physically incorrect; friction factor decreases with increasing Re.64 / NRe: Laminar-flow Fanning correlation (f = 16/NRe); not valid for turbulent flow.

Common Pitfalls:
Mixing Fanning and Darcy conventions; applying smooth-pipe correlations to rough pipes without correction.

Final Answer:
f = 0.079 * NRe^-0.25