Relation of Pressure to Elevation

Relation of Pressure to Elevation

P = static pressure
Z = vertical distance
A = constant

In a static liquid (a body of liquid at rest), the pressure difference between any two points is in direct proportion to the vertical distance between two points. This pressure difference is due to the weight of the liquid and can be calculated by multiplying the vertical distance by the fluid density (or vertical distance x density of water x specific gravity of the fluid). In commonly used units:

P (static) = Z x Density H2O x S.G.

Unit of Measure Metric English
P kg/cm2 psi
Z meters feet
density of H20 1000 kg/m3 62.4 lb/ft
A 10,000 cm2/m2 144 in2/ft2

Example: Calculate pressure difference between two points. Vertical distance = 5.49 m (18 ft),
specific gravity = 1.23.

Metric English
P = Z x 1000 
x S.G P = Z x 62.4 
x S.G
P = 5.49 x 0.1 x 1.23 P = 18 x .433 x 1.23
P = 0.6753 kg/cm2 P = 9.59 psi

To obtain pressure in elevation units, the equation is rearranged:

Z = P static    
Density H20 x S.G.
x A

A pressure gauge reads 5.97 kg/cm2 (85 psi). The fluid has specific gravity of 0.95. What is the height of the equivalent column of fluid that would produce that same pressure?

Metric English
Z = 5.97 x 10,000 
1000 x .95
= 62.9 m Z = 85 x 144 
62.4 x .95
= 206.5 ft

Static head—The hydraulic pressure when the liquid is at rest.
Friction head—The pressure loss due to frictional losses in flow.
Velocity head—The energy in a fluid due to its velocity (e.g. head unit).
Pressure head—A pressure measured in equivalent head units.
Discharge head—The outlet pressure of a pump in operation.
Total head—The total pressure difference between the inlet and outlet of a pump in operation.
Inlet head—The positive pressure on a pump inlet.
Suction lift—The negative pressure on a pump inlet.