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Static Pressure vs. Head

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Pressure indicates the normal force per unit area at a given point acting on a given plane. Since there is no shearing stresses present in a fluid at rest - the pressure in a fluid is independent of direction.

For fluids - liquids or gases - at rest the pressure gradient in the vertical direction depends only on the specific weight of the fluid.

How pressure changes with elevation in a fluid can be expressed as

Δp = - γ Δh (1)


Δ p = change in pressure (Pa, psi)

Δ h = change in height (m, in)

γ = specific weight of fluid (N/m3, lb/ft3 )

The pressure gradient in vertical direction is negative - the pressure decrease upwards.

Specific Weight

Specific Weight of a fluid can be expressed as:

γ = ρ g (2)


ρ = density of fluid (kg/m3, slugs /ft3 )

g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)

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 = p2- p1

= - γ (h2- h1 ) (3)


p2= pressure at level 2  (Pa, psi)

p1 = pressure at level 1 (Pa, psi)

h2= level 2    (m, ft)

h1 = level 1 (m, ft)

(3) can be transformed to:

Δ p = p1 - p 2

= γ (h2- h1 ) (4)


p1 - p2= γ Δ h (5)


Δ h = h2- h1 = difference in elevation - the dept down from location h2to h1 (m, ft)


p1 = γ Δ h + p2(6)

Example - Pressure in a Fluid

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

p1 = γ Δ h + p2

= (1000 kg/m3 ) (9.81 m/s2) (10 m) + (101.3 kPa)

= (98100 kg/ms2or Pa) + (101300 Pa)

= 199400 Pa

= 199.4 kPa


ρ = 1000 kg/m3

g = 9.81 m/s2

p2= pressure at surface level = atmospheric pressure = 101.3 kPa

The gauge pressure can be calculated by setting p2= 0

p1 = γ Δ h + p2

= (1000 kg/m3 ) (9.81 m/s2) (10 m)

= 98100 Pa

= 98.1 kPa


Pressure vs. Head

(6) can be transformed to:

Δ h = (p2- p1 ) / 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 = p2- p1 .

Example - Pressure vs. Head

A pressure difference of 5 psi (lbf /in2) is equivalent to head in water

(5 lbf /in2) (12 in/ft) (12 in/ft) / (62.4 lb/ft3 )

= 11.6 ft of water

or head in Mercury

(5 lbf /in2) (12 in/ft) (12 in/ft) / (847 lb/ft3 )

= 0.85 ft of mercury

Specific weight of water is 62.4 (lb/ft3 ) and specific weight of mercury is 847 (lb/ft3 ) .

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Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.


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