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Hydraulic diameter

Hydraulic diameter extends circular-pipe relations to non-circular ducts using equivalent diameter based on wetted area and perimeter.

Опубликовано: Обновлено:

Гидравлика

Формула

$$D_h = \frac{4A}{P_w}$$
diagram Hydraulic diameter geometry

Comparison of wetted area and wetted perimeter in a non-circular conduit.

Equivalent diameter derived from A and Pw.

Обозначения

$D_h$
Hydraulic diameter, m
$A$
Wetted flow area, m^2
$P_w$
Wetted perimeter, m

Условия применения

  • Fully developed flow with defined wetted perimeter.
  • Single-phase, incompressible flow for regime and friction estimates.
  • Geometry is stable and known for perimeter and area.

Ограничения

  • Does not capture complex 3D secondary flow features in nonuniform channels.
  • For open channels with free-surface effects, use caution in selecting wetted perimeter.
  • Should be paired with regime-appropriate empirical correlations.

Подробное объяснение

This equivalent diameter makes hydraulic relations based on area-to-wall ratio consistent across shapes.

Как пользоваться формулой

  1. Find cross-sectional geometry.
  2. Compute wetted area A and wetted perimeter Pw.
  3. Substitute into D_h = 4A/Pw and reuse circular-pipe formulas.

Историческая справка

Hydraulic diameter became standard as engineers needed a single characteristic length for non-circular ducts.

Пример

For A = 0.025 m^2 and P_w = 0.45 m: D_h = 4·0.025/0.45 = 0.222 m.

Частая ошибка

Using full perimeter instead of wetted perimeter in partially filled conduits overestimates D_h.

Практика

Задачи с решением

Compute hydraulic diameter

Условие. A = 0.015 m², P_w = 0.30 m.

Решение. D_h = 4·0.015 / 0.30 = 0.20 m.

Ответ. D_h = 0.20 m.

Find perimeter from Dh and area

Условие. D_h = 0.4 m, A = 0.12 m².

Решение. Pw = 4A/D_h = 4·0.12/0.4 = 1.2 m.

Ответ. P_w = 1.2 m.

Дополнительные источники

  • Mott, R. L. (2006). Applied Fluid Mechanics.
  • Çengel, Y. A., & Cimbala, J. M. (2015). Fluid Mechanics: Fundamentals and Applications.

Связанные формулы

Инженерия

Reynolds number

$Re = \frac{\rho v D_h}{\mu} = \frac{v D_h}{\nu}$

Reynolds number indicates the ratio of inertial to viscous forces in a fluid and is used to determine flow regime.

Инженерия

Darcy–Weisbach head loss

$h_f = f\frac{L}{D_h}\frac{v^2}{2g}$

The Darcy–Weisbach equation estimates major head loss in fully developed pipe flow using friction factor and geometric ratio.

Инженерия

Velocity from flow rate

$v = \frac{Q}{A}$

If flow rate and flow area are known, this equation yields the average velocity in the section.