2011A16 Explain the difference between viscosity and density. Outline the effects of changes in
viscosity and density on the flow of gases and liquids.

 

List:

·      Definitions

·      Relationships between viscosity/density and flow rate

·      Clinical applications

 

Definitions:

Viscosity

·   Internal friction of a fluid

·   Ratio shear stress (dyn/s) to shear rate (cm/s/cm) hence units dyn.s.cm-2

·   Shear stress: force per unit area

·   Shear rate: ratio of rate of motion of imaginary plate on surface of liquid, relative to the depth of the liquid

Density

·   Ratio mass:volume

·   Units kgm-3 or g/cm-3

Laminar flow

·   Smooth, organized flow of fluid in concentric rings

·   Likely in long, narrow tubes

·   Parabolic flow profile: fast moving in the middle, in theory stationary at the walls

·   Resistance = (8 x length x viscosity) / (π x radius4) (Poiseuille equation)

·   Pressure gradient ∝ velocity (i.e. linear)

·   Wall properties matter less due to peripheral stasis.

Turbulent flow

·   Chaotic flow

·   Likely at branching points, bends etc.

·   Square-ish flow profile (necessary to expunging the periphery)

·   Pressure gradient ∝ (density x length)/radius5

·   Pressure gradient ∝ velocity2 (i.e. exponential)

·   Wall properties (e.g. smoothness) matter more due to rapid peripheral flow.

Transitional flow

Laminar + turbulent

Reynolds number

·   Dimensionless index

·   Ratio of inertial forces to viscous forces

·   Re = (2 x radius x density x velocity) / viscosity

·   < 2000 likely laminar, >2000 likely turbulent

·   ↑Reynolds number -> ↑likelihood of turbulence if:

o  Wider tube

o  ↑ flow rate

o  ↑density

o  ↓viscosity

Entrance length

Length of tube before flow can become laminar

=0.03 x Re x diameter

 

Relationships:

 

Laminar flow

Turbulent flow

↑Viscosity

↑Resistance

↑Likelihood laminar

↑Density

↑Likelihood turbulent

↑Resistance

 

Clinical application:

 

Laminar

Turbulent

Airflow:

In small airways (from 11th generation)

·   ↓Velocity

·   ↓Diameter

·   Infrequent branching

 

->If inspiratory flow rate and RR are low, parabolic flow profile augments alveolar ventilation

In large airways

·   ↑Velocity

·   ↑Diameter

·   Frequent branching

 

->Heliox (low density gas) is used in upper airway obstruction

Blood flow

Small veins:

·   ↓Velocity

·   ↓Diameter

·   Entrance length reached

 

->Risk of thrombosis

Large arteries:

·   ↑Velocity

·   ↑Diameter

·   Branching before entrance length

 

->Important for coronary artery perfusion