Flow Resistance (Glottal Resistance)

aerodynamics measurement glottis resistance turbulence
Last updated: 2025-01-29

Flow Resistance (Glottal Resistance)

Flow resistance provides a useful metric for characterizing the relationship between pressure and flow in the respiratory system. This concept is particularly important for understanding glottal function during phonation.

Definition of Flow Resistance

Flow resistance is the ratio of pressure drop to flow rate through a constriction:

R = P/U

where:

  • R = resistance (kPa/(L/s) or Pa·s/m³)
  • P = pressure drop across constriction (kPa or Pa)
  • U = flow rate through constriction (L/s or m³/s)

Interpretation

Resistance quantifies how much pressure is required to maintain a given flow:

High resistance:

  • Large pressure needed for modest flow
  • Narrow constriction
  • Or high friction losses

Low resistance:

  • Small pressure produces large flow
  • Wide opening
  • Or smooth flow passage

Example Calculation

For typical phonation:

  • Subglottal pressure: P = 1.0 kPa
  • Airflow: U = 0.2 L/s
  • Glottal resistance: R = 1.0 kPa / 0.2 L/s = 5.0 kPa/(L/s)

Glottal Resistance

The glottis typically offers the greatest resistance in the respiratory tract:

Typical Values

Research by Netsell et al. (1991) provides normative data:

Males:

  • Average glottal resistance: 30-50 Pa·s/L
  • Range: 20-100 Pa·s/L

Females:

  • Average glottal resistance: 40-70 Pa·s/L
  • Range: 30-120 Pa·s/L

Gender difference:

  • Females show higher resistance
  • Attributed to smaller laryngeal dimensions
  • Smaller glottal area for similar flow

Factors Affecting Glottal Resistance

Unfortunately, resistance isn’t easily tabulated because it depends on many factors:

1. Glottal Area

Primary factor:

  • Smaller area → higher resistance
  • Relationship is nonlinear (roughly R ∝ 1/A²)
  • Degree of vocal fold adduction determines area

During phonation:

  • Area varies cyclically
  • Resistance peaks during closure
  • Approaches infinity at complete closure
  • Minimum during maximum opening

2. Constriction Geometry

Entry and exit shape:

  • Sharp edges increase resistance
  • Rounded edges reduce resistance
  • Asymmetry affects flow pattern

Glottal profile:

  • Convergent vs. divergent
  • Parallel-sided vs. curved
  • Vertical dimension (thickness)

3. Flow Velocity

Reynolds number dependence:

  • Low Re: laminar flow, lower resistance
  • High Re: turbulent flow, higher resistance
  • Transition zone: unpredictable behavior

4. Vocal Fold Surface

Tissue properties:

  • Smooth surface: lower resistance
  • Irregular surface: higher resistance
  • Lesions or masses increase local resistance

Reynolds Number

Engineers use Reynolds number to characterize flow regimes:

Re = (vd)/μ

where:

  • Re = Reynolds number (dimensionless)
  • v = particle velocity (m/s)
  • d = effective diameter of constriction (m)
  • μ = kinematic viscosity of fluid (m²/s)

Physical Meaning

Reynolds number represents the ratio of inertial to viscous forces:

Low Re (<2000):

  • Viscous forces dominate
  • Laminar flow: smooth, parallel streamlines
  • Predictable behavior
  • Lower resistance

High Re (>4000):

  • Inertial forces dominate
  • Turbulent flow: chaotic, mixing patterns
  • Irregular behavior
  • Higher resistance

Transition zone (2000-4000):

  • Mixed regime
  • Flow can switch between laminar and turbulent
  • Difficult to predict

Reynolds Number in Phonation

For typical glottal flow:

During phonation:

  • v ≈ 20 m/s (peak velocity)
  • d ≈ 0.003 m (3 mm effective diameter)
  • μ ≈ 1.5 × 10⁻⁵ m²/s (air at 37°C)
Re = (20 m/s × 0.003 m) / (1.5 × 10⁻⁵ m²/s)
   = 4000

This is right at the transition between laminar and turbulent flow!

Factors Influencing Reynolds Number

Increases with:

  • Higher subglottal pressure (increases v)
  • Wider glottal opening (increases d)
  • Lower air viscosity (unlikely to change)

Decreases with:

  • Lower pressure (decreases v)
  • Narrower glottis (decreases d)
  • Higher viscosity

Turbulence in Voice Production

Desired turbulence:

  • [h] sound requires turbulence
  • Fricatives ([s], [f]) require turbulence
  • Whisper involves turbulent glottal flow

Undesired turbulence:

  • Breathy voice shows excessive turbulence
  • Indicates incomplete glottal closure
  • Audible as noise component
  • Often indicates pathology or poor technique

Controlling turbulence:

  • Narrower glottis reduces Re (paradoxically)
  • But creates higher velocity
  • Trade-off between area and velocity effects
  • Optimal area depends on intended sound

Faucet Demonstration

Reynolds number effects can be observed with a faucet:

Low flow (low Re):

  • Smooth, clear stream
  • Laminar flow
  • Can see through water

Gradually increase flow:

  • Stream remains smooth initially
  • Suddenly becomes turbulent at critical flow
  • White, frothy appearance
  • Transition occurs abruptly

High flow (high Re):

  • Fully turbulent
  • Chaotic, unpredictable patterns
  • Higher energy dissipation

This demonstration shows the abrupt laminar-to-turbulent transition characteristic of Reynolds number physics.

Practical Implications

For Measurement

Flow resistance measurements are useful but must be interpreted carefully:

Considerations:

  • Varies with glottal configuration
  • Changes throughout vibratory cycle
  • Depends on phonatory task
  • Influenced by multiple geometric factors

Clinical utility:

  • Comparing pre/post treatment
  • Tracking changes over time
  • Identifying extreme values
  • Population norms (with caution)

For Voice Quality

Resistance relates to perceptual qualities:

High resistance:

  • Pressed voice quality
  • Increased effort sensation
  • Potential for vocal fatigue
  • Risk of tissue trauma

Low resistance:

  • Breathy voice quality
  • Inefficient voice production
  • Reduced intensity
  • May indicate incomplete closure

Optimal resistance:

  • Clear, efficient voice
  • Appropriate loudness with comfortable effort
  • Varies by individual and task

For Voice Training

Understanding resistance helps explain:

Why breathiness increases with:

  • Wider glottal gap
  • Incomplete adduction
  • Certain pathologies

Why pressed voice involves:

  • Excessive adductory force
  • Reduced glottal area
  • Increased resistance and effort

Imagery and technique:

  • “Flow on the breath” reduces resistance
  • “Support the tone” balances pressure and resistance
  • Efficient phonation optimizes this balance

Summary

Flow resistance R = P/U characterizes the pressure-flow relationship in constrictions. Glottal resistance depends on area (primary factor), geometry, Reynolds number, and surface properties. Reynolds number determines whether flow is laminar or turbulent, with the glottis operating near the transition region (Re ≈ 4000). While resistance values are difficult to tabulate due to multiple dependencies, the concept remains useful for clinical assessment and understanding voice production mechanisms.

Key Takeaways

  • ✅ Flow resistance R = P/U quantifies pressure required for a given flow
  • ✅ Glottal resistance varies with area, geometry, velocity, and surface properties
  • ✅ Reynolds number Re = vd/μ determines laminar vs. turbulent flow regime
  • ✅ Glottal flow operates near Re ≈ 4000, at the transition between laminar and turbulent

Further Reading

  1. Netsell, R., Lotz, W. K., Duchane, A. S., & Barlow, S. M. (1991). Vocal tract aerodynamics during syllable productions: Normative data and theoretical implications. Journal of Voice, 5(1), 1-9.
  2. Scherer, R., & Guo, C. (1991). Generalized translaryngeal pressure coefficient for a wide range of laryngeal configurations. In J. Gauffin & B. Hammarberg (Eds.), Vocal fold physiology (pp. 83-90). San Diego: Singular Publishing Group.
  3. Van den Berg, J. (1956). Direct and indirect determination of the mean subglottal pressure. Folia Phoniatrica, 8, 1-24.
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