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Unformatted text preview: Aero 311 - HomeWork #7 Read Chapter 11 Sections 1-6 Problems 11.1, 11.10, 11.17, 11.21, 11.25, 11.41 11.1 Determine the dimensions of the following quantities. / /
(a) The velocity potential, as, and the streamfunction, w.
(b) The strength of a source, Q. (c) The strength of a potential vortex, F. (d) The strength of a doublet, D. ‘ll.10 Verify by direct substitution that the velocity potential and streamfunction for a doublet, Equa-
tions (11.89) and (11.92), satisfy Laplace’s equation. = K(.1:2 — y’), where K is constant. Plot the streamlines 11.17 Investigate the streamfunction 111(21, y)
w could represent. in the full my plane, ﬁnd any stagnation points, and interpret what the ﬂo ‘ 11.21 Determine the velocity potential and streamfunction for a uniform ﬂow inclined at an angle a to
the 2: axis, i.e., for u = U(icosa +jsina). 11.25 Consider stagnation-point flow for which the Cartesian velocity components are given by u = A2:
and v = —Ay where A is a constant. (a) Determine the streamfunction, 1/2. (b) Determine the velocity potential, q). (c) Now add a source of strength Q. What must Q be in order to move the stagnation point to 1 = 0,
y = yo? (d) In general, 112 and d) are unique to within an additive constant. What must the constant for 112 be
if the dividing streamline passes through the displaced stagnation point and is deﬁned by 1/) = 0? 11.41 Consider superposition of a source of strength Q = Uh and a uniform flow of velocity U from
leﬁ to right. (a) What is the complete streamfunction for this ﬂow? Include an appropriate constant in the stream—
function to insure that the negative 2 axis is a dividing streamline along which uv = 0. (b) Locate any stagnation points that might be present.
(c) Noting that y = rsin 0, show that the body shape («12 = 0) is such that y —o ill/2 as m —+ 00. ((1) Make a qualitative sketch of what the body and streamlines look like. Be sure to include some
streamlines both inside and outside the body. ...
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This note was uploaded on 10/28/2009 for the course AERSP 311 at Penn State.