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Unformatted text preview: 20 marks QUESTION 3
The streamfunction ψ (r, θ ) = U0 r 1 − R2
r2 where U0 is constant, R is the radius of the cylinder and 0 < R ≤ r, describes
steady, two-dimensional ﬂow over a cylinder in cylindrical polar coordinates assuming that the ﬂuid is inviscid (see sketch).
r U0 R θ p0
a) Show that the cylinder surface is a streamline for this ﬂow.
i) Determine the velocity components, vr and vθ .
ii) Identify the location of the stagnation points.
iii) Show whether or not this ﬂowﬁeld is incompressible (use the conservation of
iv) Show whether or not this ﬂowﬁeld is irrotational.
c) Is this a potential ﬂow? If it exists, ﬁnd the velocity potential function φ (r, θ ).
i) Express the pressure of the ﬂuid on the surface of the cylinder as a function of
U0 , p0 and θ . Neglect the elevation change.
ii) In the present conditions, it can be found that the total drag force on the cylinder
is equal to zero. Is it what you would expect in a real ﬂow over a cylinder? Explain
brieﬂy. 4 ...
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This note was uploaded on 09/14/2011 for the course ME 362 taught by Professor Ceciledevaud during the Winter '11 term at Waterloo.
- Winter '11