Solution u=ax+,y+Cz v=a2x+b,y+C22 w=aix+bay+Cz Continuity for incompressible flow × +c=0→a1+b2+c3=0 Example 2 An incompressible velocity field u=a(x2-y,w=b, a, b are const, what v=? Solution ouX 02ax+ 0 v=-2axy+((x, t) An arbitrary function of x, z, t9 Solution 0 u v w x y z    + + =    1 1 1 u a x b y c z = + + 2 2 2 v a x b y c z = + + w a x b y c z = + + 3 3 3 1 2 3 a b c + + = 0 Continuity for incompressible flow Example 2 An incompressible velocity field: u=a(x2 -y 2 ),w=b, a,b are const,what v=? Solution 0 u v w x y z    + + =    2 0 v ax y  + =  2 v ax y  = −  v axy f x z t = − + 2 ( , , ) An arbitrary function of x,z,t