ME 450 – Fundamentals of Computational Fluid Dynamics
Instructor: Dr. Tao Xing
HOMEWORK 2
1. The general continuity in cylindrical polar coordinates is
 1 
1 

+
( r  vr ) +
(  v ) + (  vz ) = 0
t r r
r 
z
For a steady state incompressible plane flow in polar coordinates, we are given
vr = r 3 cos + r 2 sin 
Find the appropriate form of circumferential velocity v for which continuity is
satisfied assuming v = 0 on the cylindrical axis.
2. Let v be the y-component of velocity vector V and ρ be the fluid density, prove
  (  vV) = v  (  V) + (  V) v
Show step by step that this formula can be used to transform the nonconservation
form of the y component of the momentum equation

Dv
p  xy  yy  zy
=− +
+
+
+  fy
Dt
y x
y
z
to the conservation form
 ( v )
p  xy  yy  zy
+   (  vV ) = − +
+
+
+  fy
t
y x
y
z
1