# 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

Design of pumping systems and pipelines. With centrifugal pumps, displacement pumps, cavitation, fluid viscosity, head and pressure, power consumption and more.

## Related Documents

### Darcy-Weisbach Equation - Major Pressure and Head Loss due to Friction

The Darcy-Weisbach equation can be used to calculate the major pressure and head loss due to friction in ducts, pipes or tubes.

### Efficiency in Pumps or Fans

The overall pump and fan efficiency is the ratio power gained by the fluid to the shaft power supplied.

### Hydropower

Power potential vs. head and flow rate.

### Hydrostatic Pressure vs. Depth

Depth and hydrostatic pressure.

### PE, PEH and PVC Pipes - Pressure Loss vs. Water Flow Diagram

Pressure loss *(bar/100 m)* and velocy in PE, PEH or PVC pipes with water flow.

### Potential Energy - Hydropower

Elevation and potential energy in hydropower.

### Pressure Gradient Diagrams

Static pressure graphical presentation throughout a fluid flow system.

### Pressure to Head Unit Converter

Pressure vs. head units - like *lb/in ^{2}, atm, inches mercury, bars, Pa *and more.

### Pumps - Head vs. Pressure

Converting head (ft or m) to pressure (psi or bar, kg/cm2) and vice versa.

### Pumps - NPSH (Net Positive Suction Head)

An introduction to pumps and the Net Positive Suction Head (NPSH).

### Pumps - Parallel vs. Serial Arrangement

Adding head and flowrate for pumps arranged in parallel vs. serial.

### Pumps - Suction Head vs. Altitude

The suction head of a water pump is affected by its operating altitude.

### Pumps and Fans - Energy Equation and Head Rise

The energy equation can be used to calculate the head rise in pumps and fans.

### System Curve and Pump Performance Curve

Utilize the system curve and the pump performance curve to select the proper pump for a particular application.

### Types of Fans - Capacity Ranges

Centrifugal, axial and propeller fans and their capacity ranges.

### Velocity Pressure Head

Dynamic pressure or velocity head.

### Water Pressure vs. Head

Pressure in pounds per square inch (psi) vs. head in feet of water (ft h2o).