# The Squeeze is Pressure

## Reaching the primary standard accuracy requires compensating for a large number of factors

##### By Keith Cheatle

The calibration of pressure instrumentation is one of the most common types of calibration that takes place in laboratories and industrial facilities.

The calibration equipment for moderately accurate calibrations is relatively inexpensive, rugged, and easy to use.

The wide range of pressures in one facility will probably require more than one type or range of calibration standard. The pressure range from 1 inch of water to 100,000 pounds per square inch, for example, represents a 2.77 million to one ratio of maximum pressure to minimum pressure.

The number of standards needed increases if vacuum and absolute pressure calibrations are required and if various fluids such as water, oil, and gas are required.

Pressure is a derived unit based on the fundamental units of length (l), mass (m), and time (t). Earlier sections defined pressure as a force acting on an area (l2), defined force as an accelerated mass (m), and defined acceleration as (l/t2).

The accuracy of many of the pressure standards depends on how accurately we can produce, maintain, and measure these fundamental units when manufacturing and using the standards.

Dead weight testers are the most widely used type of pressure calibrator and are available in a variety of accuracies, fluid types, ranges, and pressure units.

A typical dead weight tester consists of a fluid filled chamber that a hand pump, ram screw, or some external force pressurizes. A vertical cylinder together with a close fitting piston that rotates within the cylinder is part of the chamber wall so the fluid pressure acts on the bottom area of the piston.

A pressure port in the chamber allows the connection of the pressure instrument. The fluid pressure acting on the bottom area of the piston produces an upwards \force that lifts the piston. The upward force balances out the downward force produced by the addition of weights to the top of the piston.

This force—the weight—is equal to the mass of the weights + the mass of the cylinder × the acceleration due to gravity. When the two forces are equal, the piston will float within the cylinder.

Upward force = pressure × piston area

Downward force = mass × acceleration due to gravity = weight

At balance (piston floating)

Upward force = Downward force

Pressure × piston area = weight

Pressure = weight ÷ piston area

Piston and cylinder assemblies come with extremely small annular gaps between the two parts. The fluid fills this gap and acts as a lubricating film between the two surfaces.

This film reduces wear and friction between the two parts, and any axial viscous friction caused by the film reduces by slowly spinning the weights and piston at the balance point.

A tiny amount of the fluid will eventually escape past the piston, and the piston will slowly sink within the cylinder. The use of a trimming ram screw that provides a small increase in pressure to raise the piston again compensates for this leakage.

The basic accuracy of a dead weight tester stems from how accurate the measurements of the piston area and the mass of the weights are. The accuracy of testers ranges from 0.1% of reading for basic working standards to 0.003% of reading for a primary standard.

Reaching the primary standard accuracy requires compensating for a large number of factors such as local gravity, air buoyancy, temperature, air density, fluid surface tension, and piston/cylinder deformation under high pressure.

The calculation of these effects usually takes place using a computer program supplied by the tester manufacturer. The major effect that should be accounted for in lower accuracy tester is the variation in gravity since this directly affects the weight value of the masses.

The pressure range covered by dead weight testers is from approximately 5 psi to 100,000 psi, although it would require more than one tester to cover the entire range.

The weight of the piston and weight carrier assembly determines the minimum pressure since this is the minimum weight that can float. Absolute pressure calibrations are carried out using a tester that has the weights and piston in an enclosure that is evacuated to as close as possible to a perfect vacuum.

Vacuum calibrations use a tester that is essentially upside down and uses a variable vacuum source to lift the piston and the suspended weights to a floating position.

A typical working standard dead weight tester might have two interchangeable piston and cylinder assemblies with different piston areas and a range of weights that would allow the tester to cover the range from 5 to 10,000 psi.

The piston areas would be 0.1 square inch for the low range operation and 0.01 square inch for the high range operation. Each piston and weight carrier would have a weight of 0.5 pounds.

A weight set would be as follows:

• Four weights at 0.5 pounds
• Four weights at 2.0 pounds
• One weight at 9.5 pounds
• Nine weights at 10.0 pounds

Using the 0.1 square inch piston, the minimum pressure would come by floating just the piston and weight carrier, which weigh 0.5 pounds.

The resulting pressure would be 0.5 ÷ 0.1 = 5 psi

Adding one 0.5-pound weight to the weight carrier would increase the total weight to 1.0 pounds, and the resulting pressure at balance would be 1.0 ÷ 0.1 = 10 psi. Additional 0.5-pound weights result in an increase of 5 psi per weight.

Adding 2.0-pound weights result in an increase in pressure of 2.0 ÷ 0.1 = 20 psi per weight.

The 9.5-pound weight is there for convenience since the weight plus the piston and carrier weigh 9.5 + 0.5 = 10.0 pounds. This combination results in a pressure of 10.0 ÷ 0.1 = 100 psi. Each additional 10.0-pound weight will increase the pressure by 10.0 ÷ 0.1 = 100 psi.

The total weight of all the weights plus the piston and weight carrier is 110.0 pounds. This combination would result in a pressure of 110.0 ÷ 0.1 = 1,100 psi.

Using this set of weights and the 0.1 square inch piston, any pressure between 5 psi and 1,100 psi in increments of 5 psi is possible.

If the 0.01 square inch piston is used, the minimum pressure produced by floating just the piston and weight carrier is 0.5 ÷ 0.01 = 50 psi. Adding weights as above will produce pressures that are 10 times higher than those produced by the 0.1 square inch piston. The same set of weights and the 0.01 square inch piston will produce any pressure between 50 and 11,000 psi in 50-psi increments.

The incremental pressure steps also make the dead weight tester difficult or impossible to use to determine transducer characteristics such as hysteresis and linearity since the pressure is increasing and decreasing as the weights add on and move off.

Overshooting the calibration points is also common unless one uses great care when adding weights or increasing pressure.

Other considerations when using dead weight testers include making sure the tester is leveled and eliminating or accounting for errors produced by locating the instrument above or below the reference height of the tester.

The height of liquid will cause an error equal to the height times the density of the fluid. The reference level of most dead weight testers is at a plane through the center of the vertical travel of the piston.

The main concern in the maintenance of dead weight testers is keeping the tester free of dirt and debris. External dirt can change the mass of weights while dirt and debris in the tester fluid can prevent internal check valves from closing, plug small orifices, and even enter the small clearance between the piston and cylinder.

This can cause binding or surface scoring and the eventual need to scrap an expensive component. The instrument seeing calibration should be as clean as possible prior to attachment to the tester for calibration. Filters are available for some testers to reduce the introduction of dirt and debris into the tester fluid.

## Manometers are primary

In theory, a manometer is a primary standard since it measures pressure by using the fundamental units of length and mass. In practice, there are many factors that limit its use as a practical calibration tool.

The simplest form of a manometer is the U-tube manometer. This is glass tubing in the shape of a 'U' with liquid partially filling the tube. With equal pressure applied to each leg, the height of the liquid in the one leg will be equal to the height in the other leg.

If a pressure applies to the right leg, the height of the liquid will fall in the right leg and rise in the left leg. The pressure is equal to the ratio of the force applied to the surface area of the liquid in the tube.

Pressure = Force ÷ Area

Applying more pressure will cause the level in the right leg to fall further and cause the level in the left leg to rise further. Further changes in pressure show us the difference in height between the two legs is proportional to the applied pressure.

This difference in height of the liquid causes a force equal to the mass of liquid times the acceleration due to gravity, which equals the force created by the pressure on the fluid area.

F = m × g

This force distributes across the cross-sectional area of the tube producing a pressure that is equal to the applied pressure.

Pressure = (m × g) ÷ Area

The mass of liquid is equal to the volume times the density and the volume in the tubing is equal to the cross-sectional area times the height.

This results in:

Pressure = (density × Area × height × g) ÷ Area

or

Pressure = (density × height × g)

This equation shows the maximum pressure measurable by a manometer with a reasonable length has limits the density of the fluid dictates.

Using mercury as the fluid, a 100-inch manometer can only measure approximately 49 psi. Using water as the fluid, a 100-inch manometer can measure approximately 3.6 psi. This relatively narrow range is one of the disadvantages of manometers.

The fact that the pressure reading is proportional to density means corrections for density changes with temperature are necessary. Temperature can also change the length of the scale that serves to measure the fluid height.

Other disadvantages include the difficulty in reading the fluid height due to parallax errors and difficulty in keeping the internal tube walls clean.

Keith Cheatle is an ISA life member and a registered professional engineer. He worked for the Instrumentation Section of Atomic Energy of Canada Limited for 37 years. His new book is Fundamentals of Test Measurement Instrumentation, ISA Press, 2006 (www.isa.org/books).

## FAST FORWARD

• Dead weight testers are the most widely used type of pressure calibrator.
• Pressure standards are available that use highly accurate and stable pressure transducers as the reference elements.
• Low cost digital manometers that use transducers to measure pressure have largely replaced the liquid manometer.

## Terminology

Annular: shaped like a ring

Axial: along, or parallel to, the main axis; lengthwise, longitudinal

Viscous friction is stickiness in a liquid, gel, or emulsion. It represents a "resistance to flow."

Hysteresis is the maximum difference in output for any given input (within the specified range) when the value is approached first with increasing, and then with decreasing, input signals.

Linearity is the closeness of a calibration curve to a specified straight line. Linearity is the maximum deviation of any calibration point from a specified straight line during any one-calibration cycle.

Repeatability is the precision with which repeat measurements of the same sample give the same value with all conditions unchanged between measurements except time.

Piezoresistive: The piezoresistive effect describes the changing electrical resistance of a material due to applied mechanical stress. If you bend a material that has electricity flowing through it, the resistance of the material to that electrical flow changes.

## RESOURCES

Pressure relief: Hybrid instruments overcome complex issues with simple solutions.

Dynamic simulation proves pressure control system: Flexibility in pipeline operations introduces significant performance demands on its entire pressure control system.

Calibration calisthenics