Pressure Drop Calculator

Comprehensive guide to understanding and calculating pressure drops in hydraulic systems using the Darcy–Weisbach equation.

This module evaluates the pressure drop in a pipe using the Darcy–Weisbach equation. Internally all calculations use SI units. Inputs may be supplied in either metric or imperial units.

Governing Equation

ΔP = f × (L/D) × (ρv²/2)

Where:

  • ΔP – pressure drop (Pa)
  • f – Darcy friction factor (dimensionless)
  • L – pipe length (m)
  • D – pipe diameter (m)
  • ρ – fluid density (kg/m³)
  • v – average velocity (m/s)

Velocity is obtained from the volumetric flow rate Q as:

v = 4Q / (πD²)

Friction Factor

Turbulent flow friction factor is estimated using either:

Haaland Equation (Explicit)

1/√f = -1.8 × log₁₀[(ε/D/3.7)¹·¹¹ + 6.9/Re]

This explicit equation provides a good approximation for turbulent flow and is computationally efficient.

Colebrook–White Equation (Implicit)

1/√f = -2 × log₁₀(ε/3.7D + 2.51/Re√f)

This implicit equation is more accurate but requires iterative solution methods.

Laminar Flow

f = 64/Re

For laminar flow (Re < 2300), the friction factor is independent of surface roughness.

Assumptions

  • Incompressible, single-phase flow
  • Steady state and fully developed flow
  • Constant fluid properties

References

  1. 1.
    White, F.M. Fluid Mechanics, 8th ed. McGraw-Hill, 2016.
  2. 2.
    Haaland, S.E. "Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow." Journal of Fluids Engineering, 105(1), 1983.
  3. 3.
    Colebrook, C.F., and White, C.M. "Experiments with Fluid Friction in Roughened Pipes." Proceedings of the Royal Society A, 161(906), 1937.

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