4. Consider a velocity field V = K(yi + xk) where K is a constant. The vorticity, Qz , is (A) -K (B) K (C) -K/2 (D) K/2

a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.

Question 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v = -Upxy i+ Upxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines.

PLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2)

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This question is from the subject "Fluid Mechanics"