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Инженерия / Гидравлика

Velocity from flow rate

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

Опубликовано: Обновлено:

Гидравлика

Формула

$$v = \frac{Q}{A}$$
calculation-grid Flow-to-velocity conversion

Numeric substitution showing velocity as discharge divided by area.

One-step conversion between discharge and average velocity.

Обозначения

$v$
Average flow velocity, m/s
$Q$
Volumetric flow rate, m^3/s
$A$
Flow area, m^2

Условия применения

  • Flow is single-phase, incompressible, and steady over the measurement interval.
  • Average flow area is defined for the section.
  • Area and discharge units are consistent.

Ограничения

  • May deviate from local peak velocity in nonuniform distributions.
  • Not valid when the section has partial filling unless A is effective wetted area.
  • Needs correction for roughness or profile effects in highly sheared turbulent flows.

Подробное объяснение

Rearranging the continuity definition for one section gives v as the ratio of discharge to area.

Как пользоваться формулой

  1. Confirm area corresponds to the actual wetted cross section.
  2. Use consistent SI units for Q and A.
  3. Compute v directly from division.

Историческая справка

This inversion form is routinely used in practical engineering to move between pump curves, pipe sizing, and measured discharge.

Пример

Q = 0.3 m^3/s and A = 0.15 m^2 -> v = 0.3/0.15 = 2.0 m/s.

Частая ошибка

Do not use full pipe area in partially full channels or open conduits.

Практика

Задачи с решением

Find velocity

Условие. Q = 0.12 m^3/s, A = 0.04 m^2.

Решение. v = Q/A = 0.12/0.04 = 3 m/s.

Ответ. v = 3 m/s.

Find required area

Условие. Q = 0.09 m^3/s, v = 1.5 m/s.

Решение. A = Q/v = 0.09/1.5 = 0.06 m^2.

Ответ. A = 0.06 m^2.

Дополнительные источники

  • Fox, R. W., Pritchard, P. J., & McDonald, A. T. (2011). Introduction to Fluid Mechanics, 8th ed.
  • Çengel, Y. A., & Cimbala, J. M. (2015). Fluid Mechanics: Fundamentals and Applications.

Связанные формулы

Инженерия

Flow rate

$Q = A v$

Flow rate is the volume of fluid passing through a cross-section per unit time. For idealized one-dimensional flow, it is the product of area and average velocity.

Инженерия

Continuity equation

$A_1 v_1 = A_2 v_2 = Q$

For steady incompressible flow in a pipe network or conduit, the mass flow continuity implies that discharge is the same at all sections.

Инженерия

Hydraulic diameter

$D_h = \frac{4A}{P_w}$

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