Question

2. For 3D Rankine half-body generated by the combinations of the uniform stream and a three- dimensional source at the origin, answer the followings; $$phi = Ux - frac{m}{4pi} frac{1}{sqrt{x^2 + y^2 + z^2}} = Ur cos heta - frac{m}{4pi r}$$ (1) Show that the limiting radius far downstream is $r = (m/pi U)^{1/2}$. (Hint: Far downstream the fluid from the source must move with velocity U for the pressure to balance across the dividing streamline.) (2) Show that the distance from the source to the stagnation point is one half of the limiting radius far downstream. (3) Find the body's radius in the plane x = 0. (Hint: Use the dividing streamline through the stagnation point.)

          2. For 3D Rankine half-body generated by the combinations of the uniform stream and a three-
dimensional source at the origin, answer the followings;
$$phi = Ux - frac{m}{4pi} frac{1}{sqrt{x^2 + y^2 + z^2}} = Ur cos 	heta - frac{m}{4pi r}$$
(1) Show that the limiting radius far downstream is $r = (m/pi U)^{1/2}$. (Hint: Far downstream
the fluid from the source must move with velocity U for the pressure to balance across the
dividing streamline.)
(2) Show that the distance from the source to the stagnation point is one half of the limiting
radius far downstream.
(3) Find the body's radius in the plane x = 0. (Hint: Use the dividing streamline through the
stagnation point.)

$2. For 3D Rankine half-body generated by the combinations of the uniform stream and a three- dimensional source at the origin, answer the followings; phi = Ux - fracm4pi frac1sqrtx^2 + y^2 + z^2 = Ur cos heta - fracm4pi r (1) Show that the limiting radius far downstream is r = (m/pi U)^1/2. (Hint: Far downstream the fluid from the source must move with velocity U for the pressure to balance across the dividing streamline.) (2) Show that the distance from the source to the stagnation point is one half of the limiting radius far downstream. (3) Find the body's radius in the plane x = 0. (Hint: Use the dividing streamline through the stagnation point.)$

Added by Darren F.

Question

Please give Ace some feedback