Pressure, Level, and Flow Measurement

Pressure, Level, and Flow Measurement

Introduction

This chapter covers the three physical quantities most commonly measured in industrial instrumentation: pressure, level, and flow. For the Red Seal exam, you must master not only the physical principles, but also calibration calculations, technology selection, and Canadian regulatory requirements. Each section presents the essential definitions, conversion formulas, installation procedures, and typical pitfalls.

1. Pressure Measurement

1.1 Definitions and Units

Pressure is defined as the force exerted per unit area: P = F/A. In instrumentation, three references are distinguished:

Legal units in Canada: the pascal (Pa) and its multiples (kPa, MPa). Common conversions to memorize:

Absolute/gauge pressure conversion formula:

P_abs = P_gauge + P_atm

1.2 Sensor Technologies

1.2.1 Bourdon Tube Sensor

The Bourdon tube deforms under the effect of pressure; this deformation is transmitted to a sector gear that drives a pointer. Typical accuracy: ±0.5% to ±2% of full scale. Limitation: not suitable for rapid dynamic measurements or very low pressures.

1.2.2 Diaphragm Sensor

A metallic or ceramic diaphragm deforms; the deformation is detected by a strain gauge (piezoresistive) or capacitive variation. Advantages: good accuracy (±0.1%), fast response, compatible with corrosive fluids if the diaphragm is coated.

1.2.3 Piezoelectric Sensor

Used for dynamic measurements (pulsations, explosions). Not suitable for static measurements (charge leakage). Very rigid, high resonant frequency.

1.2.4 Resonant Quartz Sensor

High accuracy (±0.01%), used in metrology and laboratory applications. High cost.

1.3 Calibration and Calculations

Pressure transmitter calibration procedure:

Linearity error formula:

Linearity (%) = (Maximum deviation / Full scale) × 100

Calculation example: A 0-100 kPa transmitter displays 49.2 kPa for a reference pressure of 50 kPa. The error is: (49.2 – 50) / 100 × 100 = –0.8%. If the tolerance is ±0.5%, the transmitter is out of specification.

1.4 Regulatory Requirements

The Canadian Electrical Code, Part I (CE Code) (C22.1-21) applies to electrical installations in classified areas. For pressure transmitters installed in hazardous locations, you must verify:

Common pitfall: confusing operating pressure with design pressure. The design pressure (MAWP – Maximum Allowable Working Pressure) is the maximum allowable pressure at design temperature; it is always higher than the normal operating pressure.

2. Level Measurement

2.1 General Principles

Level measurement can be continuous (analog value) or discrete (threshold detection). Methods are divided into:

2.2 Differential Pressure (DP) Measurement

This is the most common method for liquids in open or closed tanks.

Principle: The hydrostatic pressure at the measurement point is P = ρ × g × h, where ρ is the liquid density (kg/m³), g = 9.81 m/s², and h is the liquid height (m).

Open tank: the DP transmitter measures the gauge pressure at the bottom. The range is calculated as follows:

ΔP_max = ρ × g × h_max

Closed tank under pressure: the low-pressure (LP) side is connected to the top of the tank to compensate for vapor pressure. The measurement becomes:

ΔP = P_bottom – P_top = ρ × g × h

Wet leg problem: if the LP line is filled with liquid (condensate), an additional pressure is added. The range must be shifted negative.

Formula with wet leg:

ΔP = ρ_liquid × g × h – ρ_leg × g × L

where L is the height of the wet leg.

Example: Tank 2 m high, liquid ρ = 1000 kg/m³, wet leg filled with water (ρ = 1000 kg/m³), L = 2.5 m.

Range: ΔP_min = 0 – 1000 × 9.81 × 2.5 = –24,525 Pa

ΔP_max = 1000 × 9.81 × 2 – 24,525 = –4,905 Pa

The transmitter must be configured for a range of –24.5 kPa to –4.9 kPa.

2.3 Float and Displacer Measurement

The float follows the liquid surface; the displacer uses Archimedes' principle: the buoyancy force varies with the immersed level.

Archimedes' formula:

F_buoyancy = ρ_liquid × V_immersed × g

For a cylindrical displacer with total volume V and cross-sectional area A: the measured force varies linearly with level h:

F = ρ × A × h × g

Pitfall: if the liquid density changes (temperature variation, mixture), the measurement is distorted. Compensation is required, or another technology should be selected.

2.4 Radar and Ultrasonic Measurement

Distance formula for radar/ultrasonic:

d = (c × t) / 2

where c is the propagation speed (3 × 10⁸ m/s for radar, ~343 m/s for ultrasonic at 20 °C) and t is the round-trip time.

2.5 Capacitive Measurement

A probe and the tank wall form a capacitor. The capacitance depends on the level:

C = (2 × π × ε × L) / ln(D/d)

where ε is the permittivity of the medium, L is the immersed length, D is the outer diameter, and d is the probe diameter.

Requirement: the liquid must have a dielectric constant significantly different from that of the gas (air ≈ 1). Calibration must be performed with the actual liquid.

3. Flow Measurement

3.1 Definitions and Units

Volumetric flow rate Q (m³/s, L/min, gpm) is the volume of fluid passing through a cross-section per unit time. Mass flow rate Q_m (kg/s, lb/min) is the mass per unit time. Relationship:

Q_m = ρ × Q

Average velocity: v = Q / A, where A is the pipe cross-sectional area (m²).

Reynolds number:

Re = (ρ × v × D) / μ

where D is the internal diameter (m) and μ is the dynamic viscosity (Pa·s).

3.2 Differential Pressure Flowmeters (Primary Elements)

3.2.1 Orifice Plate

The most common type. The pressure drop ΔP is related to flow by:

Q = C_d × A_o × √(2 × ΔP / ρ)

where C_d is the discharge coefficient (≈0.6 for a standard plate) and A_o is the orifice cross-sectional area.

Quadratic relationship: flow is proportional to the square root of ΔP. Practical consequence: at 25% of maximum flow, the DP is only 6.25% of maximum DP. Accuracy degrades at low flow rates.

Installation requirements (ISO 5167):

3.2.2 Venturi Tube

Lower permanent pressure loss than the orifice plate. Used for large flow rates and dirty fluids.

3.2.3 Flow Nozzle

Compromise between orifice plate and Venturi. Good accuracy, moderate pressure loss.

General formula for all primary elements:

Q = K × √(ΔP)

where K is a calibration constant that includes C_d, A_o, ρ, and geometric factors.

3.3 Electromagnetic Flowmeters (Magmeters)

Based on Faraday's law: the induced voltage is proportional to the fluid velocity.

E = B × L × v

where B is the magnetic flux density (T), L is the distance between electrodes (m), and v is the velocity (m/s).

Operating conditions:

Advantage: no pressure loss, measurement independent of density and viscosity.

3.4 Turbine Flowmeters

A rotor spins at a speed proportional to the flow rate. The pulse frequency is measured:

Q = f / K_factor

where K_factor is the K-factor (pulses per litre or per m³).

Accuracy: ±0.5% to ±1% of reading. Sensitivity: viscosity affects linearity; calibration must be performed with the service fluid.

3.5 Vortex Flowmeters

A bluff body generates alternating vortices. The vortex frequency is proportional to velocity:

f = St × v / d

where St is the Strouhal number (≈0.2 for standard geometries) and d is the bluff body width.

Limitation: the Reynolds number must be > 20,000 for a stable signal. Not suitable for low flow rates or highly viscous fluids.

3.6 Coriolis Mass Flowmeters

Direct measurement of mass flow rate through the deformation of an oscillating tube. Accuracy: ±0.1% to ±0.2% of reading. Independent of density, temperature, and viscosity. High cost, significant pressure loss.

3.7 Ultrasonic Flowmeters

ΔT = (2 × L × v) / c²

Advantage: non-intrusive (clamp-on sensors). Limitation: accuracy depends on the flow profile and transducer alignment.

3.8 Flow Conversion Calculations

Volumetric flow conversion:

1 m³/h = 16.667 L/min = 4.403 gpm

1 L/min = 0.2642 gpm

Mass flow conversion:

Q_m (kg/h) = Q (m³/h) × ρ (kg/m³)

Example: A flowmeter indicates 500 L/min of water (ρ = 1000 kg/m³). The mass flow rate is:

Q_m = 0.5 m³/min × 1000 kg/m³ = 500 kg/min = 30,000 kg/h

3.9 General Installation Requirements

4. Measurement Loops and Signal Transmission

4.1 4-20 mA Current Loop

The standard instrumentation signal: 4 mA = minimum value, 20 mA = maximum value. Advantages: the loop is self-powered, insensitive to voltage drops (if the loop resistance is within limits), and break detection is possible (0 mA).

Calculating the measured value:

Physical_value = (I – 4) / 16 × (Range_max – Range_min) + Range_min

Example: 0-100 kPa transmitter, measured current = 12 mA.

P = (12 – 4) / 16 × 100 = 50 kPa

Maximum loop resistance:

R_max = (V_supply – V_min_transmitter) / I_max

With V_supply = 24 V, V_min = 10 V, I_max = 20 mA:

R_max = (24 – 10) / 0.020 = 700 Ω

4.2 Digital Protocols

Pitfall: on a HART loop, the loop resistance must be ≥ 250 Ω for the digital signal to be readable by the communicator.

5. Applicable Canadian Standards

Rule 8-200 of the Canadian Electrical Code, Part I: concerns raceways and conductors in classified areas. You must know the minimum distances and permitted cable types.

6. Commissioning and Maintenance Procedures

6.1 Pressure Transmitter Commissioning

6.2 Common Troubleshooting

6.3 Safety

7. Pitfalls to Avoid

8. Summary

9. Self-Assessment Questions (Red Seal Type)

10. Normative References

This chapter covers the essential knowledge required for the Red Seal exam in instrumentation and control. Review the formulas, redo the calculations by hand, and practice on the self-assessment questions before moving on to the next step.