Fill This Form To Receive Instant Help

Help in Homework
trustpilot ratings
google ratings


Homework answers / question archive / Boundary Layer I HW #2 Instructor: M

Boundary Layer I HW #2 Instructor: M

Mechanical Engineering

Boundary Layer I

HW #2 Instructor: M. Behbahani-Nejad.

1. A certain flow given by u = y5, v = -x2, w = 0 has a temperature field given by T = y + t2x. Calculate the local time-rate of change of T at (1, 2), and also the material derivative of T at (1, 2) at any time t. From this last result, what conclusions can you draw?

2. The trajectories of the fluid particles in a particular flow are specified by

        x = x0et,     y = x0 + (y0 – x0)e-2t

 (a) Sketch a few trajectories in the x - y plane for different values of x0 and y0

(b) Obtain the Lagrangian velocities by differentiating the x and y function above w.r.t time.

(c) By elimination (x0, y0) between the trajectory equations above and the velocity components, obtain expressions for u and v in terms of (x, y, t); this constitude the Eulerian velocity components for this flow.

3. A compressible fluid is caused to flow through a tube of constant diameter in such a way that the velocity along the axis is given by

             u = u1 + u2/2 + u2 – u1/2 tanh x

Where u1 and u2 are the velocities when x is minus or plus infinity, respectively. The density does not change with time at any point. The density at x = - ¥ is r = r1. Obtain an equation for the distribution of density along the tube.

4. Computation algorithms for Navier-Stokes equations are often expressed in column-vector notation. For Cartesian coordinates, the divergence form of the Navier-Stokes equations can be written as:

      U/t + E/x + F/y + G/z = 0

Where U, E, F and G are 5-element column vectors. Show that

U =

r

ru

rv

rw

Et

 

E =

ru

P + ru2 - txx

ruv - txy

ruw - txz

(Et + P)u - utxx - vtxy - wtwz + qx

and give the corresponding forms for F and G.

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE

Related Questions