Humidity, Volume, and Flow

Humidity and Moisture Metrology

Humidity defines water vapor content in a gas mixture. Relative humidity (%RH) is the ratio of water vapor partial pressure $e$ to the saturation vapor pressure $e_w(T)$ at that gas temperature:

$$\%\text{RH} = \frac{e}{e_w(T)} \times 100\%$$

Humidity Instrumentation

• Chilled Mirror Hygrometers (Calibrated Optical Reference): A gas sample flows across a polished rhodium or platinum mirror cooled by a thermoelectric Peltier cooler. A light source reflects off the mirror into an optical photodetector. When the mirror cools to the gas condensation temperature, dew or frost forms, scattering light. An analog or digital servo loop controls mirror temperature to maintain a constant condensate layer thickness. The mirror temperature, measured by a calibrated embedded miniature PRT, gives the true dew point ($T_d$) or frost point ($T_f$). Below freezing, establish whether the condensate is liquid water or ice. Dew point and frost point correspond to different saturation vapor-pressure relations; the temperature difference is not a fixed 0.5°C across a range. Determine phase and use the appropriate relation and uncertainty.
• Capacitive Thin-Film Polymer Hygrometers: Fast-response field instruments. A thin hygroscopic polymer film changes dielectric constant as water vapor is absorbed. Susceptible to hysteresis between wetting and drying cycles, and temperature-dependent drift.
• Aspiration Psychrometers: Utilize paired thermometers—one dry bulb measuring ambient temperature, and one wet bulb wrapped in a wetted cotton wick. Forced air aspiration ($\ge 3\text{ to }5\text{ m/s}$) produces evaporative cooling. Relative humidity is derived from the dry-wet depression, barometric pressure, and psychrometric tables.
• Saturated Salt Solutions (ASTM E104): Sealed enclosures containing saturated salt slurries in equilibrium with air generate fixed, reproducible relative humidity values at $25^\circ\text{C}$:
  • Lithium Chloride ($\text{LiCl}$): $11.3\% \pm 0.3\%$
  • Magnesium Chloride ($\text{MgCl}_2$): $32.8\% \pm 0.2\%$
  • Sodium Chloride ($\text{NaCl}$): $75.3\% \pm 0.1\%$
  • Potassium Chloride ($\text{KCl}$): $84.3\% \pm 0.3\%$
  • Potassium sulfate is an example of a high-humidity salt reference near 97.3% RH at 25°C. Use the evaluated temperature-dependent value and uncertainty; salt composition, equilibration, contamination, and temperature gradients affect realized humidity.
  • Rule: Slurries must maintain excess solid undissolved crystals, and enclosure temperature must remain strictly isothermal (a $1^\circ\text{C}$ temperature difference between liquid and air induces up to $6\%\text{RH}$ error).

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Fluid Flow Measurement

Fluid flow characterizes the motion of liquids and gases in closed conduits. Calibration technicians distinguish between Volumetric Flow ($Q$) and Mass Flow ($\dot{m}$):

$$\dot{m} = \rho \cdot Q$$

Closed-Conduit Flowmeter Technologies

Coriolis Mass Flow Advantages

Coriolis meters represent a major advancement in fluid metrology. When fluid travels through vibrating tubes (excited at natural resonance by an electromagnetic drive coil), the fluid mass experiences Coriolis accelerations directed opposite to the vibration at the inlet and in the direction of vibration at the outlet. The resulting twist creates a phase/time shift ($\Delta t$) between upstream and downstream optical or magnetic pickoff sensors. The phase shift is directly proportional to true mass flow, less dependent on a developed velocity profile than many volumetric meters. Temperature, installation stress, entrained gas, two-phase flow, zero stability, and fluid conditions can still affect results; follow the meter’s documented limits.

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Fluid Volume Calibration and the Gravimetric Method

Liquid volume standards include volumetric flasks, transfer pipettes, burettes, and graduated cylinders.

• Class A and Class B: Consult the applicable glassware standard, vessel type, capacity, material, reference temperature, and to-contain/to-deliver designation. Some standards give Class A half the Class B tolerance, but that relationship and one glass composition are not universal for every volumetric item. Use actual certificate corrections and uncertainty when needed.
• TC ("To Contain" / In): Calibrated to contain the specified volume at $20^\circ\text{C}$ (e.g., volumetric flasks).
• TD ("To Deliver" / Ex): Calibrated to deliver the specified volume at $20^\circ\text{C}$, accounting for the wetting film adhering to the internal walls (e.g., pipettes, burettes).

Gravimetric Calibration of Piston Pipettes (ISO 8655)

Under ISO 8655, micro-pipettes are calibrated gravimetrically using an analytical balance, high-purity degassed distilled water, and an evaporation trap.

Use the gravimetric conversion appropriate to the apparatus. Density and air-buoyancy terms convert weighed water mass to volume; a thermal-expansion factor applies only when the validated method requires normalization of the apparatus to a reference temperature. Do not apply a glassware expansion factor indiscriminately to piston pipettes. The following illustrates such a reference-temperature model:

$$V_{20} = (m_L - m_E) \times Z$$

Where:

• $m_L - m_E$ = net apparent mass of dispensed water (loaded mass minus tare mass)
• $Z$ = conversion factor combining water density at temperature $t$, air buoyancy, and container thermal expansion:

$$Z = \frac{1}{\rho_w(t) - \rho_a} \left( 1 - \frac{\rho_a}{\rho_b} \right) \left[ 1 - \gamma (t - 20^\circ\text{C}) \right]$$

Where:

• $\rho_w(t)$ = density of pure water at calibration temperature $t$
• $\rho_a$ = air density based on barometric pressure, temperature, and relative humidity
• $\rho_b$ = density of balance calibration weights ($8000\text{ kg/m}^3$)
• $\gamma$ = cubical thermal expansion coefficient of the pipette material

Pipetting technique

Use the method and manufacturer guidance for the pipette volume, liquid, tips, and aspiration/dispense mode. Prewetting, vertical aspiration, immersion depth, dwell, blowout, and contact with the receiving vessel can affect delivered volume. Do not prescribe one angle or immersion depth for every instrument. Record water temperature, evaporation controls, weighing conditions, and the selected gravimetric conversion.