Flow, Humidity and Composition Instruments

Flow Measurement

Flow rate quantifies the volume or mass of fluid passing through a pipe per unit time. Monitoring flow is critical for calculating thermal heat balances, controlling fuel-to-air combustion ratios, and regulating boiler feedwater delivery.

Flowmeters are grouped into Differential Pressure, Mechanical, and Electronic instruments.

1. Differential Pressure (DP) Flowmeters

DP meters operate on Bernoulli's Principle and the Law of Conservation of Mass (Continuity). When fluid encounters a cross-sectional restriction inside a closed pipe, its velocity increases ($v_2 > v_1$). By Bernoulli's equation, this acceleration produces a corresponding drop in static pressure ($P_1 > P_2$):

$$Q = C_d \cdot A_2 \sqrt{\frac{2 \Delta P}{\rho (1 - \beta^4)}}$$

Where $Q$ is volumetric flow, $C_d$ is the discharge coefficient, $A_2$ is the throat area, $\rho$ is fluid density, $\Delta P = P_1 - P_2$, and $\beta = d / D$ is the diameter ratio.

• The Square Root Relationship: Flow rate is proportional to the square root of differential pressure: $Q \propto \sqrt{\Delta P}$. Conversely, differential pressure is proportional to the square of flow: $\Delta P \propto Q^2$. If flow increases to $100\%$, $\Delta P$ is $100\%$; if flow drops to $50\%$, $\Delta P$ drops to $25\%$ ($0.5^2$). Therefore, an electronic square root extractor must be applied in the transmitter or control system to linearize the flow signal for indication and control.
• Primary Differential Elements:
  • Orifice Plate: A thin, flat metallic plate with a precisely machined hole clamped between two pipe flanges. Concentric orifice plates feature a centered circular hole with a sharp, square $90^\circ$ upstream edge. Eccentric and segmental plates place the opening at the top (to pass entrained gas bubbles in liquids) or bottom (to pass entrained condensate in wet steam or sediment in slurries). Orifice plates are low-cost and easy to replace, but create high permanent pressure head loss ($40\%\text{ to }80\%$ of generated $\Delta P$).
  • Venturi Tube: Consists of a smooth converging cone ($21^\circ$), a narrow cylindrical throat, and a gradual diverging recovery cone ($5^\circ\text{ to }7^\circ$). The gradual diverging section decelerates the fluid smoothly, preventing flow separation and turbulence. Venturi tubes recover $85\%\text{ to }90\%$ of the pressure drop, resulting in very low permanent head loss ($10\%\text{ to }15\%$). They handle dirty fluids and slurries, but are physically bulky and expensive.
  • Flow Nozzle: Features a smooth elliptical convergence ending in a short cylindrical throat, but omits the diverging recovery cone. It provides intermediate permanent pressure loss ($30\%\text{ to }50\%$) and exhibits superior erosion resistance in high-velocity, high-temperature boiler feedwater and main steam piping.

2. Mechanical Flowmeters

• Turbine Flowmeters: Contain a multi-bladed axial rotor mounted on low-friction tungsten carbide bearings inside the flow path. Fluid velocity drives the rotor at an angular speed strictly proportional to volume flow. An external magnetic pickup coil mounted on the pipe exterior senses the passage of ferromagnetic rotor blade tips, generating electrical AC voltage pulses. Highly accurate for clean, low-viscosity fluids (feedwater, fuel oil), but vulnerable to bearing wear and fluid particulate damage.
• Positive Displacement (PD) Flowmeters: Feature precision-machined mechanical chambers (e.g., oval gears, oscillating pistons, nutating discs) that physically entrap discrete, known volumes of fluid and advance them downstream with each revolution. Highly accurate for viscous fluids (heavy fuel oil, lubricating oils) and independent of flow velocity profiles, but induce substantial pressure drop and can seize if solids enter the mechanism.

3. Electronic Flowmeters

• Electromagnetic Flowmeters (Magmeters): Operate on Faraday's Law of Electromagnetic Induction: a conductive fluid flowing through an applied magnetic field generates an electrical voltage perpendicular to both the flow direction and the magnetic field:

$$E = B \cdot v \cdot D$$

Where $E$ is induced voltage, $B$ is magnetic field strength, $v$ is fluid velocity, and $D$ is pipe diameter. Magmeters feature a non-magnetic pipe lined with insulating material (PTFE or neoprene) and two flush electrodes. They introduce no inserted restriction and relatively low added pressure loss, handle slurries, and provide linear output. However, the fluid must be electrically conductive ($> 5\text{ }\mu\text{S/cm}$); magmeters cannot measure steam, hydrocarbons, or pure demineralized water.

• Ultrasonic Flowmeters: Use pairs of piezoelectric transducers to measure the time difference between acoustic pulses transmitted diagonally upstream and downstream. Fluid motion accelerates downstream pulses and retards upstream pulses. The transit time difference ($\Delta t$) is directly proportional to flow velocity. Available as external clamp-on transducers, allowing non-intrusive installation without pipe penetration.
• Coriolis Mass Flowmeters: Utilize one or two vibrating flow tubes oscillated at their natural resonant frequency by an electromagnetic drive coil. Fluid flowing through the vibrating tube experiences Coriolis acceleration, which exerts opposing twisting forces on the inlet and outlet sections of the tube. Electromagnetic pickoff coils detect the resulting angular phase shift (twist angle) between the tube ends. This twist is directly proportional to true mass flow rate ($\dot{m}$), without requiring a volumetric-flow times density calculation, within the instrument’s operating and compensation limits. Coriolis meters also calculate fluid density directly from changes in tube resonant frequency; they represent the industry standard for boiler fuel oil and chemical custody transfer.

Humidity and composition measurements

Relative humidity compares water-vapour partial pressure with saturation vapour pressure at the same temperature. Heating air without adding water can lower relative humidity while the water content remains essentially unchanged. A wet-bulb/dry-bulb psychrometer uses evaporative cooling and the relevant chart; wick condition, airflow and pressure affect the result. A capacitive humidity sensor changes electrical capacitance as moisture affects its sensing layer. Dew point is the temperature at which condensation begins for the stated vapour content and pressure; compressed-air pressure dew point must be interpreted at that pressure.

Composition instruments measure a particular constituent or chemical property. A pH electrode responds to hydrogen-ion activity and needs suitable calibration and temperature consideration. Conductivity indicates ionic conduction, not a unique identification of which ions are present. An oxygen analyzer may use paramagnetism or a heated zirconia cell. Zirconia voltage follows a temperature-dependent logarithmic oxygen partial-pressure ratio; it is not simply linear in oxygen concentration. Infrared analyzers identify absorbing gases at selected wavelengths. Sample conditioning, moisture, contamination and calibration determine whether the reported value represents the process.

Source notes

Official scope and technical references checked 2026-10-17: Reference 1; Reference 2. Archived DOE handbooks are used for physical principles, not current Canadian legal requirements.