1. Group 1 Stream Function Project
Javiro Watley, Will James, Vince Tello

2. Fluid flows toward a square sink
Fluid flows toward a square sink. Neglecting what happens in the sink, show that this flow field is irrotational. Find the stream function for this system (Hint: Consider each part separately.

3. Sink with flow coming in from all sides:
Region II
-V2
-V1
Region I
Region I V1 V2
Region II

4. For irrotational flow, XU=0. In rectangular coordinates,
0(Vz=0)
(vz/y - vy/z)rx + (vx/z - vz/x)ry +
(vy/x - vx/y)rz = 0
Vy=f(z)
0(Vz=0)
Vx=f(z)
Vy constant
Vx constant

5. For irrotational flow,2Y=0. In rectangular coordinates,
This is
(2Y/x2 + 2Y/y2 + 2Y/z2 =0
where Vx=Y/y and Vy=-Y/x
In Region I, Vx=V1 or -V1, Vy=0.
Vy=0=> Y/x=0 and 2Y/y2=0=>YI=my+b
YI/y=Vx=m
Then: m=-v1 for x>0
and m=v1 for x<0

6. Vx=0=> Y/y=0 and 2Y/x2=0=>YII=mx+b - YII/y=Vy=-m
In Region II, Vy=V2 or -V2, Vx=0
Vx=0=> Y/y=0 and 2Y/x2=0=>YII=mx+b
- YII/y=Vy=-m
Then: m=v2 for y>0
and m=-v2 for y<0
Note: For questions regarding this problem refer to Chapter 8 in the text.