2. Find the rate of deformation for a line vortex with velocity field V=YG x² + y² Ans. E = -8 39 2xyG ¯(x² + y²)²³² xyG (x² + y²)² ¹6 = 6₁² = 0 yz -,&=0,8 = xG j, G=const.

The flow field about a rotating cylinder with the radius a can be modelled by superimposing the velocity potentials of a uniform flow filed, a doublet and a potential vortex: p = Ux[1+ (a/r)²] – (TO)/(2x) Does this velocity potential satisfy the Laplace equation? True False

If the velocity field is given by V = axi – ayj, and a is a con- stant, find the circulation around the closed curve shown in Fig. 2 . 6- y (1, 2) (2, 2) (1, 1) (2, 1) Fig. 2

Find the two-dimensional velocity potential ϕ ( r , θ ) for thepolar coordinate fl ow pattern υ r = Q / r , υ θ = K / r , where Qand K are constants.

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.

The velocity components in the x and y directions are given by 3 u = Axy3 - x2y, v = xy2 -- The value of a for a possible flow field involving an incompressible fluid is

I ALREADY HAVE THE ANSWER SO U DO IT AGAINE DON'T GIVE THE ANSWER THAT ALREADY POST HERE OR I WILL GIVE YOU DISLIKE

HW5_Question 3. Consider the following velocity field v = U, (x² – y² + x) ex – U, (2xy + y) e, - (b) Compute the volumetric flow rate (with a unit of m/s) through the plane at x=5 m and extending from y=0 to y=5 m and width 3 m in the z direction. The unit normal vector is in the positive x direction. Uo=2.7m/s

c. For a given velocity field calculate the constants a, b, and c such that the flow field is irrotational. V = (0.657 + 1.73x + 0.948y + az)i + (2.61 + cx + 1.91y + bz)j+(-2.73x - 3.66y – 3.64z)k