Fluid Mechanism

Glory to God" 04/04/17 if we Euterian Coust the postcles Thiday that pass enough we the execute fixed time) Space per hour the Eutrion method Kinematics (study move) with we arthosity concerned persicu, inside Bandal Method of describing fluid flow (xyysto) the observer,2 1> Lagrangion Eurorian Boat En + (obroving properties fluid as a function of time and space) x - Jobernes," * stream Line: is a line which is everywhere larges to the Velocity Vector D (dy dy = yl's V u Vector into resolving the C dx scalav u (dx) Fluid Mechanics Movies V = (uiv,w) Must Water. V = A21 rg) (Eulexian) Q. A the velocity usits of field velocity ave is given ave by mls ; re and andy are is meters; A= 0.35 (a) obtain an equation for streamlines is the Determine xy Plane: the velocity of a particle at the (b) (c) If the particle passing through time t=0, the determine poist point C (2,8) ' (xo,yo) is marked at 6 the location of the particle at time t= sec. Sol: Equation for streamline is given by m - Ay u= Ax 5 a dy = V dx u Ax V= Ay du Ky = - dx Ax dy = f(xxg) In ic; xy = C of dy = dx x lny - bnt lnow + ln(y) = (n(c) encry) =

b Velocity of particle at (2,8) V= = Axi-Ayj = 0.3x2)1 - 03(8)j = 0.6i - (2.4) i /v/ = 0.62 + (-2.4)2 = 6.12 - 2.47 mls C y 2,8,00 (2,y,t) atzi up a x An V= Axi-Ayi t = 6s. 5 at A dut No=2 , you ,6=0 A position of the particle u dn at Up= dx of Vp= du at to Sdx= = Andt no to F mg dx= Adt Th no tow ln () = A:(t:- to taking exponestial eA(+6) 2/2 = Act-to) x No 0.3(6-0) = 2 e x 12.1m

U Similarly t if dy = to S - Ay at 90 you du If Add 40 y to ln () = - A(t-to) in = A (to-t) 4 e A (to-t) = 40 4= A(to-t) 4. e 4 = 0.3 NA vs y=1.32 1.32 m