Static Pressure Head

Overview

Static pressure head is the height of a fluid column that corresponds to a given pressure. It is used to express pressure in terms of fluid column height.

Formula

$h = \frac{P}{\rho g}$

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Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Definitions

Pressure Gradient in Fluids: The rate of pressure change with vertical elevation in a static fluid, expressed as: $\Delta p = -\gamma \Delta h$ where:

• Δp = change in pressure (Pa, psi)
• Δh = change in height (m, in)
• γ = specific weight of fluid (N/m³, lb/ft³)

Specific Weight: The weight per unit volume of a fluid: $\gamma = \rho g$ where:

• ρ = fluid density (kg/m³, slugs/ft³)
• g = acceleration due to gravity (9.81 m/s², 32.174 ft/s²)

Absolute vs. Gauge Pressure: Absolute pressure is measured relative to a perfect vacuum, while gauge pressure is measured relative to atmospheric pressure ($p_{\text{atm}}$). For a fluid at depth $h$: $p_{\text{abs}} = \gamma h + p_{\text{atm}}$ $p_{\text{gauge}} = \gamma h$

Technical Details

Static Pressure in an Incompressible Fluid

For a fluid at rest, the pressure difference between two elevations is: $p_1 - p_2 = \gamma (h_2 - h_1)$ This can be rearranged to solve for pressure at depth: $p_1 = \gamma \Delta h + p_2$ where $\Delta h = h_2 - h_1$ is the depth difference.

Pressure vs. Head

Head ($\Delta h$) represents the height of a fluid column required to produce a given pressure difference: $\Delta h = \frac{\Delta p}{\gamma}$ This concept is critical in hydraulics for comparing pressure across different fluids.

Important Properties

• The pressure gradient in a static fluid is negative, meaning pressure decreases with increasing height.
• Specific weight (γ) is generally constant for liquids but varies with elevation for gases due to compressibility.
• The pressure exerted by a static fluid depends only on:
  1. Depth of the fluid
  2. Density of the fluid
  3. Acceleration due to gravity

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References

• Original Source