MEGR 3171 — Pressure Measurement

Learning Objectives

Distinguish absolute, gauge, and differential pressure and select the appropriate measurement type.
Describe the operating principle of piezoresistive, piezoelectric, and capacitive pressure transducers.
Specify a pressure transducer given range, accuracy, and frequency response requirements.
Explain static vs. dynamic pressure measurement and the role of acoustic resonance in tubing.
Identify sources of error in pressure measurement: thermal effects, zero drift, and mounting orientation.

1. Pressure Measurement Types

Absolute Pressure

Measured relative to a perfect vacuum (0 Pa). Used for atmospheric science, altitude, and thermodynamic calculations. Reference: sealed vacuum cavity.

Gauge Pressure

Measured relative to local atmospheric pressure. Used for process control, tire pressure, hydraulics. Reference: atmospheric vent port.

Differential Pressure

Difference between two process pressures. Used for flow measurement (orifice, Pitot), filter monitoring, and level measurement.

Sealed (vacuum) Reference

Absolute sensor with a sealed reference cavity. Eliminates atmospheric variation but must be calibrated at reference condition.

2. Transducer Technologies

Piezoresistive (Silicon Bridge)

The most common technology for low-to-medium pressure ranges (0 to ~1000 bar). Diffused silicon strain gauges on a thin silicon diaphragm form a Wheatstone bridge. Applied pressure deflects the diaphragm, changing gauge resistances and producing a differential output voltage. Excellent linearity, fast response, and low cost. Temperature-sensitive — requires compensation.

Piezoresistive Bridge Output

V_out = V_ex · S · P

where S = sensitivity (mV/V per full-scale pressure)
Typical: 1 to 10 mV/V FSO (full-scale output)

Piezoelectric (Charge Output)

Piezoelectric crystals (quartz, PZT) generate a charge proportional to applied pressure. High frequency response (>100 kHz) makes them ideal for dynamic measurements: shock waves, combustion, ballistics. Cannot measure DC (static) pressure — charge leaks away. Requires charge amplifier (electrometer) with very high input impedance.

Capacitive

A flexible diaphragm forms one plate of a capacitor. Deflection changes the capacitance, which is converted to voltage by an oscillator circuit. Very low temperature coefficient. Excellent for low-pressure and vacuum applications.

3. Dynamic Pressure Measurement

Pressure transducers connected by tubing to the measurement point introduce a dynamic error: the tubing and cavity form a Helmholtz resonator with a resonance frequency that can distort the measured signal. For accurate dynamic measurement:

Minimize tubing length and diameter
Mount the transducer flush with the pressure tap (no tubing)
Use a sensor with natural frequency well above the highest signal frequency

Proof Pressure vs. Burst Pressure Proof pressure is the maximum overpressure the transducer can withstand without permanent damage or output shift. Burst pressure is the absolute maximum before physical rupture. Always select a transducer with a full-scale range at least 2× the maximum expected pressure.

Practice Problems

Problem 1 — Transducer Output A piezoresistive pressure transducer has a sensitivity of 2 mV/V and a full-scale range of 0 to 200 kPa. It is excited with 10 V. What is the output voltage at 75 kPa?

Output at FSO = V_ex × S = 10 × 2 mV/V = 20 mV (at 200 kPa)

Output at 75 kPa = 20 mV × (75/200) = 20 × 0.375 = 7.5 mV

V_out = 7.5 mV at 75 kPa

Problem 2 — Transducer Selection You need to measure combustion pressure in an engine cylinder, which peaks at 8 MPa and oscillates at 800 Hz. Should you use a piezoresistive or piezoelectric sensor? Justify your answer.

Combustion pressure is a dynamic, rapidly changing signal (not static). Piezoelectric sensors are designed for dynamic measurement with high frequency response (easily handles 800 Hz). They tolerate the high temperature environment of a cylinder better. The lack of DC response is acceptable since mean pressure is not the engineering interest in combustion analysis (only the dynamic variation matters).

Piezoelectric transducer. Dynamic application, high frequency, high temperature — piezoresistive sensors drift with temperature and have lower frequency limits.