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

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

## Static pressure vs. pressure head in fluids.

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

(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

(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).

## 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.

## Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

## SketchUp Extension - Online 3D modeling!

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 Extension Warehouse!

## 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.

Temperature

oC
oF

Length

m
km
in
ft
yards
miles
naut miles

Area

m2
km2
in2
ft2
miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

6 24