. A stream function is given by: y sin where L and K are constants, 0xL and y 0. a) Does y represent a potential flow, does it obey Laplace's equation? b) What are the velocity components Vx and vy? c) If L = K = 1, locate any possible stagnation points (where x-velocity is 0). d) What do you think happens to the kinetic energy of the fluid if it is decelerated in the presence of a stationary object? What is it transformed into? To be a potential flow we must obey Laplace's equation 2 + dx dy ay 1 x L =-COS ay 1 = 1 KL v. v ???? Vx =0 K The velocity components would be X L -sin cosh COS sinh + =0 dy K y 1 (1) (+)- cosh V = ay 1 K KL y K L COS 2y 1 x X y = = sin( 7 ) cosh ( 2 )=0 K 2 y 1 = y K Vy = So, if we add up, unless K = L, the system does not obey Laplace's equation and so the flow is not a potential flow. For the flow to be incompressible, it must obey the continuity equation. V = sin cosh sin ay x (7) si 1 v =dy=sin() cosh (1) Vx K dy 1 dx = COS L sinh =0 sinh (7) si K y K If L = K = 1, locate any possible stagnation points. Look where vx = 0 because the cosh function can never be 0. sinh 2 () Incompressible x=ntL or L