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Aerodynamic Theory

T. J. Pedley, Jeffrey M. Drazen

10.1002/cphy.cp030304

Source: Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing

Originally published: 1986

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Steady Flow in a Straight Tube
1.1 Fully Developed Laminar Flow
1.2 Flow in the Entrance Region
2 Calculation of Pressure Drop
3 Dimensional Analysis—the Similarity Principle
4 Turbulent Flow in a Straight Tube
5 Effects of Changes in Geometry on Pressure and Flow
5.1 Changes in Cross‐Sectional Area—Bernoulli's Theorem
5.2 Flow in a Curved Tube
6 Flow in Branched Tubes
6.1 Laminar Inspiratory Flow
6.2 Laminar Expiratory Flow
6.3 Turbulent Flow in Branched Tubes
6.4 Pressure Drop in Branched‐Tube Systems
7 Unsteady Flow
Figure 1. Figure 1.

Development of velocity profile with distance along a tube; thickness (δ) of boundary layer increases. Numbers are values Of x/dRe at which corresponding profiles occur, where x is distance from entrance, d is tube diameter, V is fluid velocity, is average fluid velocity, and Re is Reynolds number (see Eq. 8).

Adapted from Prandtl and Tietjens 50
Figure 2. Figure 2.

Qualitative picture of flow downstream of a single symmetric bifurcation with Poiseuille flow in the parent tube. Lower branch indicates direction of secondary motions, new boundary layer, and separation region. Upper branch indicates velocity profiles in plane of the junction (solid line) and in normal plane (dashed line).
Figure 3. Figure 3.

Moody plot of friction factor (CF) against tracheal Reynolds number (Re) for inspiratory flow in a cast of major airways of human bronchial tree. Solid lines have slopes of −1, –½, and 0.

Adapted from Slutsky et al. 42
Figure 4. Figure 4.

Change in velocity profile shape as flow enters a region of pipe of smaller radius (top) and larger radius (bottom). A1, A2: cross‐sectional areas at stations 1 and 2.

From Pedley et al. 35
Figure 5. Figure 5.

Flow separation at an expansion. Note turbulence generated at edge of jet.
Figure 6. Figure 6.

A: secondary motions develop when fluid flows in a curved tube, with flow in center of tube directed toward outside of bend and returning near walls. B: axial velocity profile in plane of the bend is also distorted from Poiseuille flow (upstream) to a form having a peak near the outside wall (downstream). C: profile in transverse plane is distorted to an M shape. D: note initial skew in velocity profile when entry‐flow profile is flat.
Figure 7. Figure 7.

Asymmetric bifurcation showing some quantities that must be specified to define flow uniquely. , average velocity; d, diameter; θ, angle size; S, possible sites of flow separation.
Figure 8. Figure 8.

Streamlines in steady flow in a T junction when flow rates in the 2 daughter tubes are comparable. Solid line, streamline near wall, remaining close to it; dashed line, streamline near center line of parent tube; dashed‐dotted line, streamline between the two; S, sites of flow separation.
Figure 9. Figure 9.

Secondary motions generated in parent tube of a single bifurcation during expiratory flow.

From Schroter and Sudlow 41


Figure 1.

Development of velocity profile with distance along a tube; thickness (δ) of boundary layer increases. Numbers are values Of x/dRe at which corresponding profiles occur, where x is distance from entrance, d is tube diameter, V is fluid velocity, is average fluid velocity, and Re is Reynolds number (see Eq. 8).

Adapted from Prandtl and Tietjens 50


Figure 2.

Qualitative picture of flow downstream of a single symmetric bifurcation with Poiseuille flow in the parent tube. Lower branch indicates direction of secondary motions, new boundary layer, and separation region. Upper branch indicates velocity profiles in plane of the junction (solid line) and in normal plane (dashed line).



Figure 3.

Moody plot of friction factor (CF) against tracheal Reynolds number (Re) for inspiratory flow in a cast of major airways of human bronchial tree. Solid lines have slopes of −1, –½, and 0.

Adapted from Slutsky et al. 42


Figure 4.

Change in velocity profile shape as flow enters a region of pipe of smaller radius (top) and larger radius (bottom). A1, A2: cross‐sectional areas at stations 1 and 2.

From Pedley et al. 35


Figure 5.

Flow separation at an expansion. Note turbulence generated at edge of jet.



Figure 6.

A: secondary motions develop when fluid flows in a curved tube, with flow in center of tube directed toward outside of bend and returning near walls. B: axial velocity profile in plane of the bend is also distorted from Poiseuille flow (upstream) to a form having a peak near the outside wall (downstream). C: profile in transverse plane is distorted to an M shape. D: note initial skew in velocity profile when entry‐flow profile is flat.



Figure 7.

Asymmetric bifurcation showing some quantities that must be specified to define flow uniquely. , average velocity; d, diameter; θ, angle size; S, possible sites of flow separation.



Figure 8.

Streamlines in steady flow in a T junction when flow rates in the 2 daughter tubes are comparable. Solid line, streamline near wall, remaining close to it; dashed line, streamline near center line of parent tube; dashed‐dotted line, streamline between the two; S, sites of flow separation.



Figure 9.

Secondary motions generated in parent tube of a single bifurcation during expiratory flow.

From Schroter and Sudlow 41
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Article Title: Aerodynamic Theory
 

How to Cite

T. J. Pedley, Jeffrey M. Drazen. Aerodynamic Theory. Compr Physiol 2011, Supplement 12: Handbook of Physiology, The Respiratory System, Mechanics of Breathing: 41-54. First published in print 1986. doi: 10.1002/cphy.cp030304