Dimensional analysis : the great principle of similitude / Jeffrey H. Williams.

Format:

Book

Author/Creator:

Williams, Jeffrey H. (Jeffrey Huw), 1956- author.

Contributor:

Institute of Physics (Great Britain), publisher.

Rosengarten Family Fund.

Language:

English

Subjects (All):

Dimensional analysis.

Mathematical physics.

Physical Description:

1 volume (various paginations) : illustrations 27 cm

Place of Publication:

Bristol, UK : IOP Publishing 2021

Contents:

Machine generated contents note: 1. The origin of units

1.1. The systeme internationale des unites (the SI)

Further reading

Reference

2. A brief history of dimensional analysis: a holistic approach to physics

2.1. Homogeneity of units

2.2. Geometry of motion

2.3. Derived units

2.4. Fourier and the nature of physical quantities

2.5. Dimensional arguments

References

3. Introduction to dimensions

3.1. Dimensional formulae

3.2. Conversion from one system of units to another system of units

3.2.1. The consequences of mixing units

3.3. Dimensional homogeneity

3.3.1. Checking equations for dimensional consistency

3.3.2. Some details: [x] represents the physical dimension of a

3.4. Approaching dimensional analysis

3.4.1. Checking a formula

3.4.2. Deriving a formula

4. Why, and how we play with variables

4.1. The de-dimensionalization of equations

4.2. Some of the more widely-used nondimensional groups

4.3. Some examples of straightforward dimensional analyses

4.3.1. The Trinity explosion

4.3.2. The smallest measurement-scale

4.3.3. The fine-structure constant

4.3.4. Drop spatter analysis

5. The Buckingham II - theorem and its application

5.1. The Buckingham n-technique

5.2. Some examples of dimensional analysis involving the n-theorem

5.2.1. Dimensional analysis of a soap bubble

5.2.2. Lift generated by a wing

5.2.3. Flows in pipes, tubes and blood vessels

6. Scaling and similitude

6.1. Astronomy and the music of the spheres

6.1.1. Dimensional analysis of Kepler's third law

6.2. Dimensional analysis of the pendulum: the first precision measuring device

6.3. Harmonic oscillations

7. Rules of thumb, intuitive planning and physical insight

7.1. Dimensional variables

7.2. Nondimensional variables

7.3. Eliminating a variable you suspect could be negligible: the design of golf-balls

7.4. The Rayleigh-Riabouchinsky Paradox

8. Continuum forces

8.1. The basic concepts of fluid mechanics

8.2. Drag forces

8.2.1. Similitude

8.2.2. The calculus of velocity-dependent frictional forces

8.2.3. Dimensional analysis of the drag force

8.2.4. A car on a highway

8.2.5. The skydiver

8.2.6. Stokes' law

8.3. Bubbles in fizzy drinks

8.4. Magnetic-braking: the terminal velocity of a magnet falling in a tube of a non-magnetic metal

9. Why is the sky blue?

9.1. Quantifying light intensity: subjectively and in absolute terms

9.2. Polarizability

9.2.1. Dimensional analysis applied to intermolecular forces

9.3. Rayleigh scattering

9.4. Collision-induced light scattering

10. The equilibrium between matter and energy

10.1. Black-body radiation and dimensional analysis

10.2. The displacement law of Wilhelm Wien

10.3. The cosmic microwave background

11. Dimensions involving molecules and fields

11.1. Polarization and magnetization

11.2. Electromagnetic fields

11.3. Dimensional homogeneity in electrostatics

11.4. Molecules and fields

11.5. Interacting magnetic dipoles, and the origin of radiation at 21 cm

11.6. Units and the SI

11.7. Final point: electro- and magneto-optics

12. The dynamics of atoms and molecules

12.1. Rutherford's model of the hydrogen atom

12.2. The earliest quantum view of the atom

12.3. Electric dipole transitions

12.3.1. The effect of an electric field-gradient on allowed rotational spectra

12.4. Melting in organic solids

13. Modelling phenomena

13.1. Prototypes

13.2. Experimental design and interpretation

13.2.1. Scaling the prototype of a submarine

13.2.2. Modelling boats

13.3. Dimensional analysis of a water sport

14. The great principle of similitude in biology and sport

14.1. Scaling of flight

14.2. Walking and running with dinosaurs

14.3. Constructing the best First-VIII

14.4. How much can you lift?

15. A miscellany of analyses by dimension

15.1. Dimensional analysis of cooking

15.2. Black holes

15.3. The Aeolian harp

15.4. The final frontier of dimensional analysis: the Drake equation.

Notes:

Includes bibliographical references.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

9780750336536

0750336536

OCLC:

1335885031