# Method of Measuring Strain, Pressure, and Flow Rate

Strain is the deformation, either expansion or compression, of a material due to a force acting on it. For example, a metal rod or bar will lengthen slightly when an appropriate force is applied, as illustrated in Figure 1(a).

Also, if a metal plate is bent, there is an expansion of the upper surface, called tensile strain, and a compression of the lower surface, called compressive strain, as shown in Figure 1(b).

## Method of Measuring Strain

Strain Gauge: Strain gauges are based on the principle that the resistance of a wire increases if its length increases and decreases if its length decreases. This is expressed by the following formula:

R = ρL/A

This formula states that the resistance of a wire depends directly on the resistivity and the length (L) and inversely on the cross-sectional area (A).

A strain gauge is basically a long very thin strip of resistive material that is bonded to the surface of an object on which strain is to be measured, such as a wing or tail section of an airplane under test. When a force acts on the object to cause a slight elongation, the strain gauge also lengthens proportionally and its resistance increases.

Most strain gauges are formed in a pattern similar to that in Figure 2(a) to achieve enough length for a sufficient resistance value in a smaller area. It is then placed along the line of strain as indicated in Figure 2(b).

## The Gauge Factor of a Strain Gauge

An important characteristic of strain gauges is the gauge factor (GF), which is defined as the ratio of the fractional change in resistance to the fractional change in length along the axis of the gauge.

For metallic strain gauges, the GFs are typically around 2. The concept of gauge factor is illustrated in Figure 3 and expressed in following Equation.

Where R is the nominal resistance and ΔR is the change in resistance due to strain. The fractional change in length (ΔL/L) is designated strain (ε) and is usually expressed in parts per million, called microstrain (µε designated).

## Basic Strain Gauge Circuits

Because a strain gauge exhibits a resistance change when the quantity it is sensing changes, it is typically used in circuits similar to those used for RTDs. The basic difference is that strain instead of temperature is being measured.

Therefore, strain gauges are usually applied in bridge circuits or in constant-current-driven circuits, as shown in Figure 4. They can be used in applications in the same way as RTDs and thermistors.

The 1B31 is an example of a strain gauge signal conditioner. The 1B31 includes an instrumentation amplifier, a low-pass filter, and adjustable transducer excitation.

## Method of Measuring Pressure

Pressure transducers are devices that exhibit a change in resistance proportional to a change in pressure. Basically, pressure sensing is accomplished using a strain gauge bonded to a flexible diaphragm as shown in Figure 5.

When a net positive pressure exists on one side of the diaphragm, the diaphragm is pushed upward and its surface expands. This expansion causes the strain gauge to lengthen and its resistance to increase.

Pressure transducers typically are manufactured using a foil strain gauge bonded to a stainless steel diaphragm or by integrating semiconductor strain gauges (resistors) in a silicon diaphragm. Either way, the basic principle remains the same.

Pressure transducers come in three basic configurations in terms of relative pressure measurement. The absolute pressure transducer measures applied pressure relative to a vacuum, as illustrated in Figure 6(a).

The gauge pressure transducer measures applied pressure relative to the pressure of the surroundings (ambient pressure), as illustrated in Figure 6(b).

The differential pressure transducer measures one applied pressure relative to another applied pressure, as shown in Figure 6(c).

Some transducer configurations include circuitry such as bridge completion circuits and op-amps within the same package as the sensor itself, as indicated.

## Pressure Measuring Circuits

Because pressure transducers are devices in which the resistance changes with the quantity being measured, they are usually in a bridge configuration as shown by the basic op-amp bridge circuit in Figure 7(a). In some cases, the complete circuitry is built into the transducer package, and in other cases the circuitry is external to the sensor.

The symbols in parts (b) through (d) of Figure 7 are sometimes used to represent the complete pressure transducer with an amplified output. The symbol in part (b) represents the absolute pressure transducer, the symbol in part (c) represents the gauge pressure transducer, and the symbol in part (d) represents the differential pressure transducer.

## Pressure Transducer Applications

Pressure transducers are used anywhere there is a need to determine the pressure of a substance.

• In medical applications, pressure transducers are used for blood pressure measurement;
• in aircraft, pressure transducers are used for altitude pressure, cabin pressure, and hydraulic pressure;
• in automobiles, pressure transducers are used for fuel flow, oil pressure, brake line pressure, manifold pressure, and steering system pressure, to name a few applications.

## Method of Measuring Flow Rate

One common method of measuring the flow rate of a fluid through a pipe is the differential-pressure method. A flow restriction device such as a Venturi section (or other type of restriction such as an orifice) is placed in the flow stream.

The Venturi section is formed by a narrowing of the pipe, as indicated in Figure 8. Although the velocity of the fluid increases as it flows through the narrow channel, the volume of fluid per minute (volumetric flow rate) is constant throughout the pipe. Because the velocity of the fluid increases as it goes through the restricted area, the pressure also increases.

If pressure is measured at a wide point and at a narrow point, the flow rate can be determined because flow rate is proportional to the square root of the differential pressure, as shown in Figure 8.