206-Question1.80.sagews

Question1.80

Find an expression for the streamlines of the flow and sketch a few lines

from pylab import *

theta = 0.5
cset = [-2,-1,0,1,2]

x = arange(-2.1,2.1,0.01)

clf()

for c in cset:
    y = tan(theta)*x + c
    plot(x,y,label='C='+str(c))

legend()
axis([-2,2,-2,2],)
grid()

savefig('1.80.png')

Question 1.83

Find the time-varing streamlines which pass though reference point (x0, y0)

from pylab import *

timeslot = [-0.4,-0.2,0,0.5,1.0]
x = arange(0,2.1,0.01)

clf()
for t in timeslot:
    y = x**(1+2*t)
    plot(x,y,label='t='+str(t)[0:4]+'s')
legend(loc='upper left')

axis([0,2,0,2])
xlabel(r'$x/x_0$')
ylabel(r'$y/y_0$')
grid()

savefig('1.83.png')

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Question 1.84

Find the equation of the pathline which passes through the point (x0, y0)at t=0

# Scripts to plot the flow pathline in Question 1.84. Written by Aaron Zhang
# For MAE 3030 Fluid Mechanics, Department of Mechanical & Automation Engineering
# The Chinese University of Hong Kong

from pylab import *
y = arange(0.1,2,0.01)

x = exp(log(y)+log(y)*log(y))
clf()

plot(x,y)

axis([0,2,0,2])
xlabel(r'$x/x_0$')
ylabel(r'$y/y_0$')
grid()
savefig('1.84.png')