Page 21 - kursus eBook

Recall that the azimuthal velocity is reckoned positive if it is anticlockwise. Note that the
tangential velocity is a maximum at θ = ±! / 2 .

It is left as an exercise for the student to show from the velocity fields that the

streamfunction for the flow is given by,
$ R '
2
♦
! = "U sin# r " r ( (10.3.6)
&
)
%
✤
The streamlines of the flow are shown in Figure 10.3.2

y

x

Figure 10.3.2 The streamlines of potential flow past a cylinder.

One notices immediately the artificial character of the flow, in particular the fore-aft
complete symmetry. One never sees this is real life situations. When the flow approaches

a blunt body like the cylinder the flow typically separates from the body leaving a

♦
The mathematically sophisticated student might notice that the construct
! " i# produces an analytic function of the complex variable z=x+iy.
✤
The solution is not unique. A constant circulation around the cylinder can be added for
#
which ! = " ( ) .
2$

Chapter 10 15