2. Show that the coordinates (x,y) of the stagnation point A in the figure is V....

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2. Show that the coordinates (x,y) of the stagnation point A in the figure is V. x = -h cot YA = 0 3. Derive the expression for the stagnation streamline ABC shown in Fig. 4. Voo by ******* 2 X Source sheet with X=Constant (5) Fig. 4. Flow formed by the superposition of a uniform freestream and a straight source panel placed along the y axis. Problem 3: Consider the flow formed by the superposition of a uniform freestream V and a source panel shown in Fig. 4. J More formulas: Appendix: Useful Mathematical Formulas cos0 1 d + (b-t) t d + (b-t) t(b-t) d + (b 1) where b and d are constants. dt Va dt d dx d dx d dx X sin x + cosx = 1 -1 -(tan x): = -ln(x): dt -(tan()) X 7- 2 a + x -dx = = 1 + cos(20) 2 1 a 1 - 1+x b -1 tan tan -y x + y tan -td tan X = dx = = - In(a a + x X 1 a 1 t 1 (7) + 2 / m [d + (6 - 1) ] In d -In(a+x) b 1 ( b = ) - 1/2 [d + (6 1)] In tan^' (ax) dx =x tan^ (ax) __ln(1 + ax) 2a -1 X [ ln(x + a)dx =x ln(x + a) 2x+2a tan a a -1 [Tax + (2) dx = x tan " (# )+ - (1 + 5 ) -1 Stan =x a +ln X X a (1) (2) (3) (4) 2. Show that the coordinates (x,y) of the stagnation point A in the figure is V. x = -h cot YA = 0 3. Derive the expression for the stagnation streamline ABC shown in Fig. 4. Voo by ******* 2 X Source sheet with X=Constant (5) Fig. 4. Flow formed by the superposition of a uniform freestream and a straight source panel placed along the y axis. Problem 3: Consider the flow formed by the superposition of a uniform freestream V and a source panel shown in Fig. 4. J More formulas: Appendix: Useful Mathematical Formulas cos0 1 d + (b-t) t d + (b-t) t(b-t) d + (b 1) where b and d are constants. dt Va dt d dx d dx d dx X sin x + cosx = 1 -1 -(tan x): = -ln(x): dt -(tan()) X 7- 2 a + x -dx = = 1 + cos(20) 2 1 a 1 - 1+x b -1 tan tan -y x + y tan -td tan X = dx = = - In(a a + x X 1 a 1 t 1 (7) + 2 / m [d + (6 - 1) ] In d -In(a+x) b 1 ( b = ) - 1/2 [d + (6 1)] In tan^' (ax) dx =x tan^ (ax) __ln(1 + ax) 2a -1 X [ ln(x + a)dx =x ln(x + a) 2x+2a tan a a -1 [Tax + (2) dx = x tan " (# )+ - (1 + 5 ) -1 Stan =x a +ln X X a (1) (2) (3) (4)