1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

464 CHAPTER 11 • APPLICATIONS OF H ARMONIC FUNCTIONS Find the electrostatic potential (x, y) in the crescent-shaped region tha ...

11.6 • TWO- DIMENSIONAL ELECTROSTATICS 465 Find the electrostatic potential</> (x , y ) in t he infinite strip 0 < x & ...

466 CHAPTER. 11 • APPLJCATIONS OF HARMONIC FUNCTIONS (b) Find the electrostatic potential cf> (x, y) in the domain D that sat ...

11.7 • TWO-DIMENSIONAL FLUID FLOW 467 y Figure 11.47 A two-dimensional vector field. Both p and q are continuously differentiabl ...

468 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS that the line integral of the tangential component of V (x, y) along any sim ...

11.7 • TwO-DI MENSIONAL FLUID FLOW 469 Using the fact that 1/1 11 = ef>x and this equation, we find that the tangent vector t ...

470 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS y D w= S(z) ljl(x, y) = K (a) Fluid flow in a plane. (b) Fluid flow in the w ...

11.7 • Two-DIMENSIONAL FLUID FLOw 471 y Figure 11.49 A uniform parallel flow. • EXAMPLE 11.23 Consider the complex potential F ( ...

472 CHAP'l'ER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Figure 11. 51 Fluid flow a.round a. circle. where A is a positive real num ...

11.7 • Two-DI MENSI ONAL FLUID FLOW 4 7 3 by w = S ( z) is a one-to-one conformal mapping of the domain D consisting of the z pl ...

474 CHAPTER 11 • APPLICATIONS OF H ARMONIC FUNCTIONS -------~EXERCISES FOR SECTION 11.7 Consider the ideal 8uid Bow for the com ...

11.7 • TwO-DrMENSI ONAL FLUID FLOW 475 Figure 11.54 Consider the ideal fluid flow, where the complex potential is F(z) = Az~ = ...

476 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Figure 11.56 Show that F (z) = sin z is the complex potential for the ideal ...

11.8 • THE JOUKOWSKI AIRFOIL 411 Figure 11 .58 9. Consider the complex potential F (z) = -iArcsinz. (a) Show that F (z) determin ...

478 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Figure 11.60 y Image of a fluid flow under w = J (z) = z + !. z He showed th ...

T ' ' ' l J y ,' ' 11.8 • THE JOUKOWSKI AlRFOIL 479 w = J(z) IV = Sz(ZJ V l w=S)/'W) Figure 11.61 The composition mappings for J ...

480 CHAPTER 11 • APPLICATIONS OF H ARMONIC F UNCTIONS y v 2 t w =Sl\V) y! v Z = SJ<zl W=SjZ) Ro -x 20 4-0 -20 '-40 Figure 11. ...

11.8 • THE JOUKOWSKI AIRFOIL 481 y Figure U.63 The horizontal flow around the circle C1. v Flow around the airfoil. Figure 11.64 ...

482 CHAPTER 11 • APPLI CATIONS OF HARMONIC F UNCTIONS and the corresponding velocity function is V(x, y) = F'(z) = 1 - (z)-^2 - ...

11 .8 • THE .JOUKOWSKJ AIRFOIL y Aoww1 · 111 circulanon. a=I x Aoww· 1 111 circulatton. a = 2.2 ·na- 2 ·a Flow wilh circulauo -. ...