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

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.

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

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

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

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.