Fluid Flow

Rolf H. Sabersky, Allen J. Acosta, Edward G. Hauptmann, E.M. Gates. Fluid Flow: A First Course in Fluid Mechanics (4th Edition). Prentice Hall. (August 22, 1998). ISBN-13: 978-0135763728

Open up this jupyter notebook in the working directory with all your files you want to work with, with the Sage Math kernel (with sagemanifolds installed): I did this with the command:
~/Public/sage/sage -n jupyter
so that we run the sage program/command in the directory with the files you need (such as EuclideanManifold.py; otherwise, jupyter will treat as the "tree" directory to be the current working directory and you won't be able to go "up" the directory tree (EY : 20160509 please tell me otherwise).



In [6]:

    
load("EuclideanManifold.py")



In [10]:

    
R3eg = R3()
print R3eg.transit_sph_to_cart.display();
print R3eg.transit_cyl_to_cart.display();
R3eg.equip_metric()
print R3eg.g.display(R3eg.sph_ch.frame(),R3eg.sph_ch);
R3eg.g.display(R3eg.cyl_ch.frame(),R3eg.cyl_ch)









    



x = rh*cos(ph)*sin(th)
y = rh*sin(ph)*sin(th)
z = rh*cos(th)
x = r*cos(phi)
y = r*sin(phi)
z = zc
g = drh*drh + rh^2 dth*dth + rh^2*sin(th)^2 dph*dph






    Out[10]:





g = dr*dr + r^2 dphi*dphi + dzc*dzc



In [11]:

    
to_orthonormal3sph, e3sph, Jacobians3sph = R3eg.make_orthon_frames(R3eg.sph_ch)
to_orthonormal3cyl, e3cyl, Jacobians3cyl = R3eg.make_orthon_frames(R3eg.cyl_ch)
print to_orthonormal3sph.display(R3eg.sph_ch.frame(),R3eg.sph_ch);
to_orthonormal3cyl.display(R3eg.cyl_ch.frame(),R3eg.cyl_ch)









    



d/drh*drh + 1/rh d/dth*dth + 1/(rh*sin(th)) d/dph*dph






    Out[11]:





d/dr*dr + 1/r d/dphi*dphi + d/dzc*dzc



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