Darcy-Weisbach Equation Calculator

Formula first

Overview

This equation relates the energy loss of a fluid flowing through a pipe to the average velocity or volumetric flow rate, the pipe geometry, and the friction factor. It accounts for major losses caused by pipe wall friction over the total length and minor losses resulting from fittings, valves, and changes in pipe geometry. The formulation is applicable to both laminar and turbulent flow regimes, provided the appropriate friction factor is determined.

Symbols

Variables

$H_{L12}$ = $H_{L12}$

Apply it well

When To Use

When to use: Use this equation when determining the pressure drop or energy loss in a fully developed flow system within a circular conduit.

Why it matters: It is the fundamental tool for designing piping systems, ensuring that pumps are sized correctly to overcome resistance and maintain required flow rates.

Avoid these traps

Common Mistakes

• Confusing the Darcy friction factor with the Fanning friction factor (which is four times smaller).
• Neglecting to account for the variation of the friction factor with the Reynolds number in turbulent flow.

One free problem

Practice Problem

In a horizontal pipe system, if the pipe diameter is doubled while the volumetric flow rate remains constant, how does the head loss due to friction change, assuming the friction factor remains constant?

Solve for: $H_{L12}$

Hint: Examine the dependency of the head loss formula on the diameter D in the term involving $Q^2$/$D^5$.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Munson, B. R., Young, D. F., & Okiishi, T. H. (2006). Fundamentals of Fluid Mechanics. Wiley.
2. White, F. M. (2011). Fluid Mechanics. McGraw-Hill.
3. NIST CODATA
4. IUPAC Gold Book
5. Wikipedia: Darcy–Weisbach equation
6. NIST Chemistry WebBook
7. Britannica
8. Engineering Fluid Mechanics by Clayton T. Crowe, Donald F. Elger, John A. Roberson