ME3834 ‐ Fluid Mechanics Problem 2.9 Given: Steady incompressible flow in x-y plane with
Velocity field
, with
=
and
where A = 2 m/s2
and co-ordinates are in meters.
Find: (a) Equation for streamline through (x, y) = (1m, 3m)
(b) Time required for fluid particle to move from x = 1 m to x = 3 m.
Solution: ) streamline
Computing equations:
Substituting the value of
ln
Integrating
;
and
we get:
ln
C
, so
ln
ln C
C
or,
For the point ( ,
1,3 , C
Thus the equation is
1/3
y/3 -------------------------------------------- (a)
For a particle,
Adt
or
At
Integrating,
so,
Therefore time required for fluid particle to move from x = 1 m to x = 3 m is
–
/
2 ------------------------------------------ (b)
1