[領域] 高等流體力學-二維勢流理論
[來源]
[題目]
(1)
Consider a source of strengthmlocated at z = -b and a sink of strength
m located at z = b
Write down the complex potential for the resulting flow field,
adding a constant term -i*m/2 to make the streamline c=0
correspond to a certain position.
Expand the result for small values of
z/b and hence show that if b →無窮大 and m →無窮大 in such a way that
m/b →Pi*U, the resulting complex potential is that of a uniform flow of
magnitude U.That is, a uniformflow may be thought of as consisting of
a source located at -無窮大 and a sink of equal strength located at +無窮大
(2)
Write down the complex potential for the following quantities:
(a) A source of strengthm located at z =-b
(b) A source of strengthm located at z =-a^2/b
(c) A sink of strengthm located at z = b
(d) A sink of strengthm located at z = a^2/b
(e) Aconstant termof magnitude -im/2
Expand the resulting expression for small values of z/b and z^2/(ab), and
hence show that if b→無窮大and m→無窮大 in such a way that m/b→Pi*U,
the resulting complex potential is that of a uniform flow of magnitude
U flowing past a circular cylinder of radius a.
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※ 編輯: darrenmm 來自: 111.251.148.243 (10/20 16:08)