Static Pressure vs. Head

Static pressure vs. pressure head in fluids.

Specific Weight

Specific Weight of a fluid can be expressed as:

γ = ρ g (2)

where

ρ = density of fluid (kg/m ³ , slugs /ft ³ )

g = acceleration of gravity (9.81 m/s ² , 32.174 ft/s ² )

In general the specific weight - γ - is constant for fluids. For gases the specific weight - γ - varies with elevation (and compression).

The pressure exerted by a static fluid depends only upon

the depth of the fluid
the density of the fluid
the acceleration of gravity

Static Pressure in a Fluid

For a incompressible fluid - as a liquid - the pressure difference between two elevations can be expressed as:

Δ p = p ₂ - p ₁

= - γ (h ₂ - h ₁ ) (3)

where

p ₂ = pressure at level 2 (Pa, psi)

p ₁ = pressure at level 1 (Pa, psi)

h ₂ = level 2 (m, ft)

h ₁ = level 1 (m, ft)

(3) can be transformed to:

Δ p = p ₁ - p ₂

= γ (h ₂ - h ₁ ) (4)

p ₁ - p ₂ = γ Δ h (5)

where

Δ h = h ₂ - h ₁ = difference in elevation - the dept down from location h ₂ to h ₁ (m, ft)

p ₁ = γ Δ h + p ₂ (6)

Example - Pressure in a Fluid

The absolute pressure at water depth of 10 m can be calculated as:

p ₁ = γ Δ h + p ₂

= (1000 kg/m ³ ) (9.81 m/s ² ) (10 m) + (101.3 kPa)

= (98100 kg/ms ² or Pa) + (101300 Pa)

= 199400 Pa

= 199.4 kPa

where

ρ = 1000 kg/m ³

g = 9.81 m/s ²

p ₂ = pressure at surface level = atmospheric pressure = 101.3 kPa

The gauge pressure can be calculated by setting p ₂ = 0

p ₁ = γ Δ h + p ₂

= (1000 kg/m ³ ) (9.81 m/s ² ) (10 m)

= 98100 Pa

= 98.1 kPa

Pressure vs. Head

(6) can be transformed to:

Δ h = (p ₂ - p ₁ ) / γ (7)

Δ h express head - the height difference of a column of fluid of specific weight - γ - required to give a pressure difference Δp = p ₂ - p ₁ .