## Pressure Measurement in Industrial Applications

*January 7, 2012 at 8:13 am* *
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Next to temperature, pressure is the second most common measurement in process plants, and temperature and pressure measurement often go hand-in-hand in industrial applications.

Today’s high tech pressure measurement techniques are far more advanced than they were in the old days of manometers, bourdon tubes, and bellows. Modern pressure transmitters are extremely accurate and include smart electronics, built-in diagnostics, and a host of connectivity options. But one thing remains the same, and that is the physics behind the measurement.

The physical state of pressure is a difficult one to describe because it cannot be seen with the naked eye, but rest assured pressure is all around us all the time. Not only is it part of our atmosphere and hence our daily lives, but just about everything we see and touch was influenced by the forces of pressure at one time or another.

Pressure can be best described as a force which is applied uniformly over a surface, and it is measured as the force per unit area. The mathematical formula for pressure is p=F/A, where pressure equals force divided by the area.

In the international system of weights and measures, pressure is measured in Newtons per square meter. In the U.S. system of measurement, it is most commonly measured in pounds per square inch (PSI).

Pressure instruments are used to measure atmospheric pressure as an indication of weather conditions, and these measurements are expressed in inches or millimeters of mercury. The atmospheric pressure is a measurement of the weight of the air above the earth.

Low pressure areas have a lighter density of air, while high pressure areas have greater air density. The measurement is an approximation of weight in a one square inch column through earth’s atmosphere from sea level to the top of the atmosphere. Atmospheric pressure, expressed as PSIA, has a direct effect on all pressure measurements. PSIA values vary based on location in relationship to sea level and on weather conditions.

There are two commonly used measurements of pressure, both directly related to atmospheric conditions. These measurements are vacuum, or negative pressure, and gauge pressure. Vacuum is a word with a Latin origin meaning empty. It means to draw matter from a vessel in order to create pressure conditions less than atmospheric. The quality of vacuum refers to how closely the measurement approaches zero PSIA.

Gauge pressure is expressed as PSIG and is the amount of pressure in a vessel, compensated for atmospheric pressure by subtracting the atmospheric pressure from the measurement. The total pressure difference between the two is the absolute pressure.

Differential pressure, also referred to as dp, is another common industrial process measurement. This measurement is the difference in value between two pressure measurement points. A dp transmitter is generally used to measure pressure drop.

On a tank, dp is used to determine the hydrostatic head level by measuring the difference between overall pressure and the head pressure generated by the media in the tank. The difference between the two values is the hydrostatic pressure of the media. Adding compensation for the density of the media will provide a very accurate measurement of tank media level.

Another common application for a dp transmitter is to measure the differential pressure upstream and downstream of a primary flow element, usually an orifice plate. In this application, the square root of the differential pressure measurement is proportional to the flow, so the dp measurement can be used to compute the flow of the media as it passes through the primary element.

**Thermal explanation**

Because so many pressure measurement applications involve gases, it is important to consider the gas laws. In 1662, Robert Boyle proved there is an inverse relationship between pressure and volume for a fixed quantity of gas at a constant temperature. So as the volume of a gas increases, the pressure decreases, and vice versa.

Charles’s law was published in 1802 and described another important aspect of gas pressure behavior. Charles’s law states at a constant pressure, the volume of a gas and the temperature of the gas are interdependent. Gay-Lussac also played a part as his law proved at a constant volume the temperature and pressure of a gas are interdependent.

The ideal gas law is a combination of the Boyle’s law and Charles’ law, and it is a good approximation of the behavior of many gases under most conditions. Ideal gases can be described as gases where all collisions between atoms or molecules are in perfect elasticity and there are no intermolecular attractive forces.

The ideal gas law is mathematically described as pV=nRT, where p is the absolute pressure of the gas, V is the volume of the gas, n is the amount of substance of the gas in moles, R is the gas constant, and T is the temperature.

The combined gas law applies to all gases, and it mathematically brings together Boyle’s law, Charles’s law, and Gay-Lussac’s law. The combined gas law shows volume, pressure, and temperature are interdependent. The formula is expressed as pV/T=k, where p is pressure, V is volume, T is temperature, and k is a constant.

**ABOUT THE AUTHOR
**

**John Van Nostrand **is a product business manager-Pressure at Endress+Hauser. His e-mail is John.VanNostrand@us.endress.com.

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