ME2135E Fluid Mechanics II Tutorial 2
ME2135E Fluid Mechanics II Tutorial 2
ME2135E Fluid Mechanics II Tutorial 2
Bachelor of Technology
ME2135E -Fluid Mechanics II
=2.29 m/s]
(5) An incompressible flow is characterized by the stream function
=3x
2
y y
3
(a) Show that this flow is irrotational.
=
1
r
o
or
(r:) -
1
r
ou
i
o0
.
|(a) = -
Sx
2
2
+ 4y, iotational; (b) = -2x
2
+ 2y
2
, iiiotational; (c) = C0,
iiiotataional; (u) = -ln r, iiiotational]
|(a) uoes not exist; (b) = 4xy; (c) = Cln r; (u) = C0]
(b) Show that the magnitude of the velocity at any point in this flow depends only on its distance
from the origin of co-ordinates.
(c) Sketch a few streamlines for this flow in the quadrant x >0, y >0,
(d) Determine the potential function for this flow and show that the lines of constant and are
orthogonal.
(6) A two dimensional vortex of circulation r moves under its own induction in a region bounded
by a solid wall on the positive x axis and a solid wall on the positive y axis. At certain instant
the vortex centre is at the point (h, h). Find the velocity distribution along either wall and the
velocity induced at the vortex centre.
(7) A positive line vortex K is trapped in a corner, as shown in Figure below. Compute the total induced
velocity at point B (x,y) =(2a, a), and compare with the induced velocity when no walls are present.
|velocity uistiibution =
b
n
_
1
b
2
+ (x - b)
2
-
1
b
2
+ (x + b)
2
_,Inuuceu velocity =
42nb
at 1SS]
K
B
y
2a
a
0 2a
a x