Инженерия / Гидравлика
Flow rate
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.
Формула
Cross-section with area A and representative velocity v producing discharge Q through the section.
Flowrate is generated by area-averaged velocity across the section.
Обозначения
- $Q$
- Volumetric flow rate, m^3/s
- $A$
- Flow cross-sectional area, m^2
- $v$
- Average flow velocity, m/s
Условия применения
- Steady one-dimensional flow across the section.
- Velocity can be represented by an area-averaged value.
- Fluid is homogeneous and incompressible for the duration of the measurement.
Ограничения
- Does not include non-uniform velocity profiles, swirl, or secondary flows.
- Assumes no phase change and no chemical reaction in the control section.
- Not valid as a complete energy relation; only a continuity definition.
Подробное объяснение
The equation comes from conservation of volume in a differential control slice: volume swept by the flow front equals area multiplied by distance moved in time.
Как пользоваться формулой
- Identify the cross-section and compute or measure A.
- Measure or estimate the average velocity v.
- Multiply A and v to get Q.
Историческая справка
Flow rate notation Q has long been used in hydraulic engineering to represent discharge in fluid power, sewer flow, and pump calculations.
Пример
If A = 0.05 m^2 and v = 2.0 m/s, then Q = A v = 0.10 m^3/s.
Частая ошибка
A common mistake is mixing units of area in cm^2 with velocity in m/s without conversion.
Практика
Задачи с решением
Compute flow rate
Условие. A = 0.08 m^2, v = 1.5 m/s.
Решение. Q = A v = 0.08 · 1.5 = 0.12 m^3/s.
Ответ. Q = 0.12 m^3/s.
Flow rate from area and velocity
Условие. Q = 0.2 m^3/s, v = 4 m/s.
Решение. A = Q / v = 0.2 / 4 = 0.05 m^2.
Ответ. A = 0.05 m^2.
Дополнительные источники
- Fox, R. W., Pritchard, P. J., & McDonald, A. T. (2011). Introduction to Fluid Mechanics, 8th ed.
- Çengel, Y. A. (2015). Fluid Mechanics: Fundamentals and Applications, 8th ed.
- Cengel, Y. A., & Cimbala, J. M. (2015). Fluid Mechanics: Fundamentals and Applications.
Связанные формулы
Инженерия
Velocity from flow rate
If flow rate and flow area are known, this equation yields the average velocity in the section.
Инженерия
Continuity equation
For steady incompressible flow in a pipe network or conduit, the mass flow continuity implies that discharge is the same at all sections.
Инженерия
Flow rate
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.