Gas Flow

Describe the measurement of flow, pressure and volume of gases

Types of Flow:

• Laminar flow
  Fluid moving in a steady manner without turbulence.
• Turbulent flow
  Irregular fluid movement in radial, axial, and circumferential axes.
  • Laminar flow is more efficient than turbulent flow, as it requires a smaller pressure gradient to generate the same flow
  • For two fluids moving at the same speed, the velocity of individual particles in laminar flow will be both higher and lower
• Transitional flow
  Mixture of laminar and turbulent flow. Flow is typically turbulent in the centre, and laminar at the edges.

Devices used to measure gas flow include:

• Variable-Orifice Flowmeters
• Fixed-Orifice Flowmeters
  Pneumotachograph.
• Hot wire flowmeter

Note orifice based flowmeters rely on the Hagan-Poiseuille Equation:
$Q = {\Delta P r^4 \pi \over 8 \eta l}$

• Viscosity ($\eta$) and length ($l$) are fixed by both devices
• Fixed orifice flowmeters also fix radius ($r$), such that the change in pressure must therefore be proportional to flow:
  $Q= {\Delta P \pi k}$, where $k$ is a constant
• Variable orifice flowmeters also fix pressure ($\Delta P$), such that flow can be calculated from the radius:
  $Q= r^4 \pi k$

Flowmeters

Constant pressure, variable orifice flowmeters are found on wall and cylinder gases. They consist of:

• An inverse conical tube (i.e. narrower at the bottom, and wider at the top)
• A needle valve
• A bobbin
  May have a groove which causes the bobbin to spin, confirming it is not stuck.

Method:

• Gas flows from the bottom to the top of the tube
• The bobbin obstructs flow
  Therefore there is a pressure difference across it.
  • Remember: $Pressure = {Force \over Area} = {Mass \times Acceleration \over Area}$
  • At equilibrium, the pressure exerted by the bobbin on the flow of gas ($P = {Gravity \times Bobbin \ Mass \over Bobbin \ Cross-Sectional \ Area}$) is equal to the pressure exerted by the gas on the bobbin
• As flow is increased, the bobbin is pushed further up the flowmeter due to the increased pressure

• The bobbin will reach a new equilibrium position when the orifice of the flowmeter has become wide enough for the pressure on the bobbin to equal the pressure of gravity

• Flowmeters are calibrated for individual gases as:

  • Laminar (typically low flows) flow is proportional to viscosity
  • Turbulent (typically high flows) flow is proportional to density

Pros

• Cheap
• No additional power supply required
• Accurate
  Readings may be altered by:
  • Change in temperature affects viscosity and density of gas
  • Change in pressure affects density of gas

Cons

• Must be vertical
• Bobbins can become stuck

Pneumotachographs

Constant orifice, variable pressure flowmeter. Several different designs exist, and include:

• Fleisch pneumotachograph
  • Consists of several fine bore parallel tubes placed in the gas circuit
    Decreased radius and increased resistance reduces gas flow velocity, improving laminar flow.
  • A differential pressure transducer is placed at either end of the tubes
  • The pressure drop across the tubing is directly proportional to flow
• Pitot tubes
  • Consists of two tubes placed into the gas circuit:
    • One faces into the gas flow
    • The other faces away from the gas flow
  • The pressure difference between tubes is proportional to flow

Pros

• Accurate
• Continual measurement
• Allow calculation of volumes
  $Volume \ (L) = Flow \ (L.s^{-1}) \times Time \ (s)$

Cons

• Increased resistance
• Increased dead space
• Require laminar flow
  Inaccurate when:
  • Flows are higher than what the system is designed for
  • Alteration in gas density
    • Change in gas mixture
  • Alteration in gas temperature

Hot Wire Flowmeter

Components:

• Two fine platinum wires in the gas circuit
  • One heated to 180°C at OL.min^-1
  • One at 0°C
• Ammeter

Method:

• As gas flows, the wire cools
• Rate of heat dissipation is proportional to gas flow
• The amount of current required to return the wire to 180 is measured, and is proportional to flow

Pros

• Accurate
• Fast

Cons

• Fragile

References

1. Aston D, Rivers A, Dharmadasa A. Equipment in Anaesthesia and Intensive Care: A complete guide for the FRCA. Scion Publishing Ltd. 2014.