Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Static Pressure vs. Head

Static pressure vs. pressure head in fluids.

Sponsored Links

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

Δp = change in pressure (Pa, psi)

Δh = 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)

where

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:

Δp = p2 - p1

     = - γ (h2 - h1)                                     (3)

where

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:

Δp = p1 - p2

     = γ (h2 - h1)                                      (4)

or

p1 - p2 = γ Δh                                     (5)

where

Δh = h2 - h1 = difference in elevation - the dept down from location h2 to h1  (m, ft)

or

p1 = γ Δh + p2                                           (6)

Example - Pressure in a Fluid

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

p1 = γ Δh + p2

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

   = (98100 kg/ms2 or Pa) + (101300 Pa)

   = 199400 Pa

   = 199.4 kPa

where

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 Δh + p2

   = (1000 kg/m3) (9.81 m/s2) (10 m)

   = 98100 Pa

   = 98.1 kPa

Pressure vs. Head

(6) can be transformed to:

Δh = (p2 - p1) / γ                                                (7)

Δh 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).

Pressure vs. Head - Metric Units

Pressure vs. Head - Imperial Units

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Translate
About the Engineering ToolBox!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Citation

This page can be cited as

  • Engineering ToolBox, (2003). Static Pressure vs. Head. [online] Available at: https://www.engineeringtoolbox.com/static-pressure-head-d_610.html [Accessed Day Mo. Year].

Modify access date.

. .

close

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

3 30

Sponsored Links
.