LIST OF FIGURES 



Page 



gure 1 — Two successive positions of several streamlines, and paths 



of two particles 2 



gure 2 — Relation between the velocity and its components ,.. 2 



gure 3 — The equation of continuity 3 



gure i — Euler's equation of motion , 4 



gure 5 — Definition of the circulation , 6 



gure 6 — Properties of the velocity potential , 8 



gure 7 — Polar coordinates ., 10 



gure 8 — Cylindrical coordinates 11 



gure 9 — Some geometrical properties of streamlines and equipotential surfaces 13 



gure 10— Definition of the stream function ip 21 



gure 11 — Relationship between the space rate of variation of stream function 



dip/ds and particle velocity q 22 



gure 12 — Relation between particle velocities in two conjugate flows 23 



gure 13 — Curves in a doubly connected space 24 



gure 14 — Definition of the velocity potential in a doubly connected space 25 



gure 15 — Definition of the stream function in axisymmetric three-dimensional 



motion 28 



gure 16 — Kinetic energy of the fluid 29 



gure 17 — Kinetic energy of the fluid for an axisymmetric surface 31 



gure 18 — .4rgand diagram , 33 



gure 19 — The addition of two complex numbers Sj and z^ 35 



gure 20 — The product and quotient of z. and s, 35 



gure 21 — Various values of z^'^ and z^/^ 37 



gure 22 — Conformal mapping 40 



gure 23 — Correspondence of regions adjoining a curve in conformal mapping 41 



gure 24 — Maxwell's construction for curves defined by the sum of two functions ...... 42 



gure 25 — Transformation w = 1/s 43 



gure 26 — Transformation w == \/z 43 



gure 27 — Circles go into circles under transformation w = l/z • -■ 45 



