Super Position of Line Sink and Time Vortex

Gray to God" Superposition" imp of Line sink and Line Vortex The line ask bas a strongs -V/L and Lise Voter (5) both located at the origin (o) 6 4 T 4.4 a T 2 +/L The stream fusction for a source is given by I = . x/L o sake 2Th Ivortex = - T Incr) 1 vertex 2T 4= /L O - in's) 2K 27 r= exp [ ( H/ )o L - 2x4 The velocity */L 1 04 = Ur = r ac 2Th - F. 24 Uo = - or 2TR

supay custom Stream and a Doublet imp y Vs x The wistorm stream has R a located speed at Vs the and origin. the doublet has a strong superposing the stlean sino function. P= Vorsino - K r 1 sating 4=0 , when r= a in 1 we get 2 K= Vo a . rewriting equation 1 D= Yosino (r- a)) r a is a avde of radius petining 400 non dimensional O - paraseters 3 4 = I ; = a V29 r * 2 r in 2 / we get subsituting 4 P & = sino (2* 4 for rt sowing equation 2 # + (4*) it 45130 r== = 4 2 sino