Fluid Mechanism Problem

Q. The Velocity for a steady incompressible flow in the xy ^ plain is gress by V= A it Ayj, A- 2 To ,and the Co-ordinates are measured x x is meters. obtain on equation for the streamline that passes through the point (x,y) = (1,3) Calculate the time do require x=2m for fluid partle to more from x=lm in this flow field. A in + Au j. A= 2mls. you V = x , in x2 M. equation for the stream line is dy = v U5 A , x dn u. 5-5 day 1/1 du (in I'm y = Ay x2

A x2 du X - x Ay dx x dy du vi u. 5.1 dr y dr Ny du x dy x & - 20 A dix dy = dn n y eny the = lnx the line, en(+) = Inc. ft stream equation is the 4-6 constant . Now u= dx to = No = I in dt ) study x 2m A = dx Galilias x dt. transformation A (to t=H x=x'+v't 2 = 2(t-0) 4=yl VS= vw+V' Z=Z' 4 - b/w two reference pla 2 3 at range moving with womant = 2 sped wvt each of the 3-at = 0.75 to Now = ex dy at - Au dy " day. . Adt x2 After en(g) A (E-b) your at dy, the It 2/2/20 (ors) 4 enly)= 07/