# Static Pressure vs. Head

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)

where

Δ p = change in pressure (Pa, psi)

Δ h = change in height (m, in)

γ = specific weight of fluid (N/m^{ 3 }, lb/ft^{ 3 })

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)

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) *

* or *

* 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) *

* or *

* 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 } . *

#### Example - Pressure vs. Head

A pressure difference of * 5 psi (lb _{ f } /in ^{ 2 } ) * is equivalent to head in water

* (5 lb _{ f } /in ^{ 2 } ) (12 in/ft) (12 in/ft) / (62.4 lb/ft ^{ 3 } ) *

* = 11.6 ft of water *

or head in Mercury

* (5 lb _{ f } /in ^{ 2 } ) (12 in/ft) (12 in/ft) / (847 lb/ft ^{ 3 } ) *

* = 0.85 ft of mercury *

Specific weight of water is * 62.4 (lb/ft ^{ 3 } ) * and specific weight of mercury is

*847 (lb/ft*.

^{ 3 })## Related Topics

### • Fluid Mechanics

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

### • Pumps

Piping systems and pumps - centrifugal pumps, displacement pumps - cavitation, viscosity, head and pressure, power consumption and more.

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