Assignment 6.2.2. Due on 6/15/2016
1. Using potential flow theory, plot the streamlines of a uniform flow (air ρ = 1.223 kg/m3) as it flows over a long
cylinder with radius a = 2 m. The velocity of the uniform flow is U = 6 m/s. Then plot the pressure over the
surface of the cylinder as computed using Bernoulli’s equation. The upstream pressure is atmospheric (i.e.
zero).
Notice that the equation of representing the streamlines of a uniform flow over a cylinder, as studied in class is:
= 1 − Which in rectangular coordinates can also be expressed as:
=
+
1
This expression, written in MATLAB code is:
− sin
!
"
#$
+ U*sqrt(X.^2 + Y.^2).*(1 - a^2./(X.^2 + Y.^2)).*sin(atan(Y./X));
where X and Y correspond to the matrices that contain the x and y coordinates over which the stream function is
evaluated.
2. Using potential flow theory, plot the streamlines of a uniform flow as it flows over a Rankine oval. The
source/sink of the oval are located at a = ± 1.5 m with a volume flow rate per unit length of m = ± 35 m2/sec.
Determine the velocity of the uniform flow such that the total length of the oval is 2l = 8.4 m, then compute the
thickness h of the oval.
The equation that represents the streamlines of the flow over a Rankine oval is
%&'(% = −
which in MATLAB code is:
)
2
, - .
2+
+ − U*Y - m/(2*pi)*atan(2*a*Y./(X.^2 + Y.^2 - a^2));
where X and Y correspond to the matrices that contain the x and y coordinates over which the stream function is
evaluated.
Along with the plots present the code used to generate the plots
Next page shows samples of the way the plots are required to be presented.
Flow over Cylinder
Pressure Distribution over Cylinder
Flow over Rankine Oval