February 2008

Pressure points the way 

By Donald Gillum

Measurement is the first requisite of any control scheme.
Lord Kelvin summarized the significance of measurement science: "If you can measure that of which you speak and can express it by a number, you must know something of the subject. But, if you can not measure it, your knowledge is meager and unsatisfactory measurement is the basis of all knowledge." 

If you cannot measure, you cannot control. 

Pressure is a fundamental measurement from which one can infer other variables. 

Pressure values rank with those of voltage and temperature in defining the energy (primarily potential) or state of matter. Temperature is the potential for doing thermodynamic work, voltage is the potential for doing electrical work, and pressure is the potential for doing fluidic work. 

The importance of pressure measurement manifests itself by the need for transmitting signals powering equipment, inferring fluid flow in pipes, and using filled thermal systems in some temperature applications.  
We can infer liquid levels in tanks and other vessels from pressure quantities. 

Pressure is best to understand using Pascal's law, which describes the behavior of fluids at rest. According to this law, pressure is proportional to force and inversely related to the area over which the force is applied. 

In this discussion, the term "fluid" refers to both liquids and gases. Both occupy the container in which they reside; however, a liquid, if it does not completely fill the container, will present a free liquid surface, whereas a gas always fills the volume of its container. 


When a gas is in a container, molecules of the gas strike the container walls. This collision results in a force exerted against the surface area of the container. 

Pressure is equal to the force applied to an object (here, the walls of the container) divided by the area that is perpendicular to the force. The relationship between pressure, force, and area is this expression.

P = F/A

… where P is pressure, F is force, and A is area. In other words, pressure is equal to force per unit area.

For a liquid at rest, the pressure exerted by the fluid at any point will be perpendicular to the boundary point. 

In addition, whenever an external pressure applies to any confined fluid at rest, the pressure increases at every point in the fluid by the amount of the external pressure. 

The practical consequences of Pascal's law are apparent in hydraulic presses and jacks, hydraulic brakes, and pressure instruments used for measurement and calibration. 

To understand the significance of Pascal's law, consider the hydraulic press shown here. 

A force applied to the small area of piston 1 distributes equally throughout the system and applies to the large area of piston 2. 

Small forces exerted on the small piston can cause large forces on the large piston. 

The following relationship exists in the hydraulic device because the pressure at every point is equal: 

P1 = P2

Combining the two previous equations leads to the following relationships: 

P1 = F1/A1 
P2 = F2 /A2 
F1/A1 = F2 /A2 
F2 = (A2 /A1) F1


Donald Gillum (don.gillum@tstc.edu) is a Life Senior of ISA and a P.E. in Control System Engineering. He worked many years in petrochemical plants and is a master instructor at Texas State Teachers College. This article is from his book Industrial pressure, level and density measurement, ISA Press, 1995.