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Инженерия / Гидравлика

Pressure head

Pressure head converts absolute pressure to an equivalent water column height, useful for balancing energies in flow systems.

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Гидравлика

Формула

$$h_p = \frac{p}{\rho g}$$
diagram Pressure head relation

Energy interpretation of pressure converted to equivalent fluid column height.

Pressure head converts pressure magnitude into meters of fluid.

Обозначения

$h_p$
Pressure head, m
$p$
Static pressure, Pa
$\rho$
Fluid density, kg/m^3
$g$
Gravitational acceleration, m/s^2

Условия применения

  • Fluid density is approximately constant over the section.
  • Pressure is static gauge or absolute consistent with context.
  • Gravity is approximately constant.

Ограничения

  • Hydrostatic conversion only; does not include dynamic pressure terms.
  • For compressible flow density changes must be accounted for separately.
  • Large elevation differences may require total energy balance instead.

Подробное объяснение

Pressure head is a force-to-height normalization by weight density, giving a geometric representation in meters.

Как пользоваться формулой

  1. Ensure pressure data and density belong to the same fluid and condition.
  2. Apply hp = p/(rho*g).
  3. Use hp with elevation and velocity head in energy equations.

Историческая справка

The head formulation became central to practical hydraulics for pump and pipeline performance tables.

Пример

If p = 100000 Pa for water (ρ = 1000 kg/m^3) and g = 9.81 m/s^2, then hp ≈ 10.2 m.

Частая ошибка

Using gauge and absolute pressures in mixed definitions yields inconsistent head values.

Практика

Задачи с решением

Compute pressure head

Условие. p = 250000 Pa, ρ = 1000 kg/m^3, g = 9.81 m/s².

Решение. hp = 250000 / (1000·9.81) = 25.48 m.

Ответ. hp ≈ 25.5 m.

Find pressure

Условие. hp = 12 m, ρ = 1025 kg/m^3, g = 9.81 m/s².

Решение. p = ρ g h_p = 1025·9.81·12 = 120,732 Pa.

Ответ. p ≈ 120.7 kPa.

Дополнительные источники

  • Fox, R. W., Pritchard, P. J., & McDonald, A. T. (2011). Introduction to Fluid Mechanics, 8th ed.
  • Mott, R. L. (2006). Applied Fluid Mechanics.

Связанные формулы

Инженерия

Bernoulli equation (basic)

$\frac{p_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{p_2}{\rho g} + \frac{v_2^2}{2g} + z_2$

The basic Bernoulli equation links pressure head, velocity head, and elevation head along a streamline for frictionless, steady, incompressible flow.

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

Pump power

$P = \frac{\rho g Q H}{\eta}$

Pump input power equals hydraulic power raised by the pump divided by pump efficiency.